Basic Math Examples

$(c + 1) (c + 1) = (c + 1) (c - 3) \cdot 4 - 12$

Step 1

Simplify $(c + 1) (c + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + (c + 1) (c + 1) = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.2

Simplify by adding zeros.

$(c + 1) (c + 1) = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.3

Expand $(c + 1) (c + 1)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$c (c + 1) + 1 (c + 1) = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.3.2

Apply the distributive property.

$c \cdot c + c \cdot 1 + 1 (c + 1) = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.3.3

Apply the distributive property.

$c \cdot c + c \cdot 1 + 1 c + 1 \cdot 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $c$ by $c$ .

$c^{2} + c \cdot 1 + 1 c + 1 \cdot 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.4.1.2

Multiply $c$ by $1$ .

$c^{2} + c + 1 c + 1 \cdot 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.4.1.3

Multiply $c$ by $1$ .

$c^{2} + c + c + 1 \cdot 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.4.1.4

Multiply $1$ by $1$ .

$c^{2} + c + c + 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 1.4.2

Add $c$ and $c$ .

$c^{2} + 2 c + 1 = (c + 1) (c - 3) \cdot 4 - 12$

Step 2

Simplify $(c + 1) (c - 3) \cdot 4 - 12$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(c + 1) (c - 3)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$c^{2} + 2 c + 1 = (c (c - 3) + 1 (c - 3)) \cdot 4 - 12$

Step 2.1.1.2

Apply the distributive property.

$c^{2} + 2 c + 1 = (c \cdot c + c \cdot - 3 + 1 (c - 3)) \cdot 4 - 12$

Step 2.1.1.3

Apply the distributive property.

$c^{2} + 2 c + 1 = (c \cdot c + c \cdot - 3 + 1 c + 1 \cdot - 3) \cdot 4 - 12$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $c$ by $c$ .

$c^{2} + 2 c + 1 = (c^{2} + c \cdot - 3 + 1 c + 1 \cdot - 3) \cdot 4 - 12$

Step 2.1.2.1.2

Move $- 3$ to the left of $c$ .

$c^{2} + 2 c + 1 = (c^{2} - 3 \cdot c + 1 c + 1 \cdot - 3) \cdot 4 - 12$

Step 2.1.2.1.3

Multiply $c$ by $1$ .

$c^{2} + 2 c + 1 = (c^{2} - 3 c + c + 1 \cdot - 3) \cdot 4 - 12$

Step 2.1.2.1.4

Multiply $- 3$ by $1$ .

$c^{2} + 2 c + 1 = (c^{2} - 3 c + c - 3) \cdot 4 - 12$

Step 2.1.2.2

Add $- 3 c$ and $c$ .

$c^{2} + 2 c + 1 = (c^{2} - 2 c - 3) \cdot 4 - 12$

Step 2.1.3

Apply the distributive property.

$c^{2} + 2 c + 1 = c^{2} \cdot 4 - 2 c \cdot 4 - 3 \cdot 4 - 12$

Step 2.1.4

Simplify.

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Step 2.1.4.1

Move $4$ to the left of $c^{2}$ .

$c^{2} + 2 c + 1 = 4 \cdot c^{2} - 2 c \cdot 4 - 3 \cdot 4 - 12$

Step 2.1.4.2

Multiply $4$ by $- 2$ .

$c^{2} + 2 c + 1 = 4 \cdot c^{2} - 8 c - 3 \cdot 4 - 12$

Step 2.1.4.3

Multiply $- 3$ by $4$ .

$c^{2} + 2 c + 1 = 4 \cdot c^{2} - 8 c - 12 - 12$

$c^{2} + 2 c + 1 = 4 c^{2} - 8 c - 12 - 12$

Step 2.2

Subtract $12$ from $- 12$ .

$c^{2} + 2 c + 1 = 4 c^{2} - 8 c - 24$

Step 3

Move all terms containing $c$ to the left side of the equation.

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Step 3.1

Subtract $4 c^{2}$ from both sides of the equation.

$c^{2} + 2 c + 1 - 4 c^{2} = - 8 c - 24$

Step 3.2

Add $8 c$ to both sides of the equation.

$c^{2} + 2 c + 1 - 4 c^{2} + 8 c = - 24$

Step 3.3

Subtract $4 c^{2}$ from $c^{2}$ .

$- 3 c^{2} + 2 c + 1 + 8 c = - 24$

Step 3.4

Add $2 c$ and $8 c$ .

$- 3 c^{2} + 10 c + 1 = - 24$

Step 4

Add $24$ to both sides of the equation.

$- 3 c^{2} + 10 c + 1 + 24 = 0$

Step 5

Add $1$ and $24$ .

$- 3 c^{2} + 10 c + 25 = 0$

Step 6

Factor the left side of the equation.

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Step 6.1

Factor $- 1$ out of $- 3 c^{2} + 10 c + 25$ .

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Step 6.1.1

Factor $- 1$ out of $- 3 c^{2}$ .

$- (3 c^{2}) + 10 c + 25 = 0$

Step 6.1.2

Factor $- 1$ out of $10 c$ .

$- (3 c^{2}) - (- 10 c) + 25 = 0$

Step 6.1.3

Rewrite $25$ as $- 1 (- 25)$ .

$- (3 c^{2}) - (- 10 c) - 1 \cdot - 25 = 0$

Step 6.1.4

Factor $- 1$ out of $- (3 c^{2}) - (- 10 c)$ .

$- (3 c^{2} - 10 c) - 1 \cdot - 25 = 0$

Step 6.1.5

Factor $- 1$ out of $- (3 c^{2} - 10 c) - 1 (- 25)$ .

$- (3 c^{2} - 10 c - 25) = 0$

Step 6.2

Factor.

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Step 6.2.1

Factor by grouping.

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Step 6.2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 25 = - 75$ and whose sum is $b = - 10$ .

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Step 6.2.1.1.1

Factor $- 10$ out of $- 10 c$ .

$- (3 c^{2} - 10 c - 25) = 0$

Step 6.2.1.1.2

Rewrite $- 10$ as $5$ plus $- 15$

$- (3 c^{2} + (5 - 15) c - 25) = 0$

Step 6.2.1.1.3

Apply the distributive property.

$- (3 c^{2} + 5 c - 15 c - 25) = 0$

Step 6.2.1.2

Factor out the greatest common factor from each group.

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Step 6.2.1.2.1

Group the first two terms and the last two terms.

$- ((3 c^{2} + 5 c) - 15 c - 25) = 0$

Step 6.2.1.2.2

Factor out the greatest common factor (GCF) from each group.

$- (c (3 c + 5) - 5 (3 c + 5)) = 0$

Step 6.2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 c + 5$ .

$- ((3 c + 5) (c - 5)) = 0$

Step 6.2.2

Remove unnecessary parentheses.

$- (3 c + 5) (c - 5) = 0$

Step 7

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$3 c + 5 = 0$

$c - 5 = 0$

Step 8

Set $3 c + 5$ equal to $0$ and solve for $c$ .

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Step 8.1

Set $3 c + 5$ equal to $0$ .

$3 c + 5 = 0$

Step 8.2

Solve $3 c + 5 = 0$ for $c$ .

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Step 8.2.1

Subtract $5$ from both sides of the equation.

$3 c = - 5$

Step 8.2.2

Divide each term in $3 c = - 5$ by $3$ and simplify.

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Step 8.2.2.1

Divide each term in $3 c = - 5$ by $3$ .

$\frac{3 c}{3} = \frac{- 5}{3}$

Step 8.2.2.2

Simplify the left side.

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Step 8.2.2.2.1

Cancel the common factor of $3$ .

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Step 8.2.2.2.1.1

Cancel the common factor.

$\frac{3 c}{3} = \frac{- 5}{3}$

Step 8.2.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{- 5}{3}$

Step 8.2.2.3

Simplify the right side.

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Step 8.2.2.3.1

Move the negative in front of the fraction.

$c = - \frac{5}{3}$

Step 9

Set $c - 5$ equal to $0$ and solve for $c$ .

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Step 9.1

Set $c - 5$ equal to $0$ .

$c - 5 = 0$

Step 9.2

Add $5$ to both sides of the equation.

$c = 5$

Step 10

The final solution is all the values that make $- (3 c + 5) (c - 5) = 0$ true.

$c = - \frac{5}{3}, 5$

Step 11

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{5}{3}, 5$

Decimal Form:

$c = - 1.\overline{6}, 5$

Mixed Number Form:

$c = - 1 \frac{2}{3}, 5$