Basic Math Examples

$c (2 c + 4) + 2 (7 - c^{2}) = 40$

Step 1

Simplify $c (2 c + 4) + 2 (7 - c^{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$c (2 c) + c \cdot 4 + 2 (7 - c^{2}) = 40$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 c \cdot c + c \cdot 4 + 2 (7 - c^{2}) = 40$

Step 1.1.3

Move $4$ to the left of $c$ .

$2 c \cdot c + 4 \cdot c + 2 (7 - c^{2}) = 40$

Step 1.1.4

Multiply $c$ by $c$ by adding the exponents.

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Step 1.1.4.1

Move $c$ .

$2 (c \cdot c) + 4 \cdot c + 2 (7 - c^{2}) = 40$

Step 1.1.4.2

Multiply $c$ by $c$ .

$2 c^{2} + 4 \cdot c + 2 (7 - c^{2}) = 40$

$2 c^{2} + 4 c + 2 (7 - c^{2}) = 40$

Step 1.1.5

Apply the distributive property.

$2 c^{2} + 4 c + 2 \cdot 7 + 2 (- c^{2}) = 40$

Step 1.1.6

Multiply $2$ by $7$ .

$2 c^{2} + 4 c + 14 + 2 (- c^{2}) = 40$

Step 1.1.7

Multiply $- 1$ by $2$ .

$2 c^{2} + 4 c + 14 - 2 c^{2} = 40$

Step 1.2

Combine the opposite terms in $2 c^{2} + 4 c + 14 - 2 c^{2}$ .

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Step 1.2.1

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

$4 c + 14 + 0 = 40$

Step 1.2.2

Add $4 c + 14$ and $0$ .

$4 c + 14 = 40$

Step 2

Move all terms not containing $c$ to the right side of the equation.

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Step 2.1

Subtract $14$ from both sides of the equation.

$4 c = 40 - 14$

Step 2.2

Subtract $14$ from $40$ .

$4 c = 26$

Step 3

Divide each term in $4 c = 26$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 c = 26$ by $4$ .

$\frac{4 c}{4} = \frac{26}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 c}{4} = \frac{26}{4}$

Step 3.2.1.2

Divide $c$ by $1$ .

$c = \frac{26}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $26$ and $4$ .

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Step 3.3.1.1

Factor $2$ out of $26$ .

$c = \frac{2 (13)}{4}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $4$ .

$c = \frac{2 \cdot 13}{2 \cdot 2}$

Step 3.3.1.2.2

Cancel the common factor.

$c = \frac{2 \cdot 13}{2 \cdot 2}$

Step 3.3.1.2.3

Rewrite the expression.

$c = \frac{13}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{13}{2}$

Decimal Form:

$c = 6.5$

Mixed Number Form:

$c = 6 \frac{1}{2}$