Basic Math Examples

$16 c^{3} - 9 c = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $c$ out of $16 c^{3} - 9 c$ .

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Step 1.1.1

Factor $c$ out of $16 c^{3}$ .

$c (16 c^{2}) - 9 c = 0$

Step 1.1.2

Factor $c$ out of $- 9 c$ .

$c (16 c^{2}) + c \cdot - 9 = 0$

Step 1.1.3

Factor $c$ out of $c (16 c^{2}) + c \cdot - 9$ .

$c (16 c^{2} - 9) = 0$

Step 1.2

Rewrite $16 c^{2}$ as ${(4 c)}^{2}$ .

$c ({(4 c)}^{2} - 9) = 0$

Step 1.3

Rewrite $9$ as $3^{2}$ .

$c ({(4 c)}^{2} - 3^{2}) = 0$

Step 1.4

Factor.

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Step 1.4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 c$ and $b = 3$ .

$c ((4 c + 3) (4 c - 3)) = 0$

Step 1.4.2

Remove unnecessary parentheses.

$c (4 c + 3) (4 c - 3) = 0$

Step 2

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

$c = 0$

$4 c + 3 = 0$

$4 c - 3 = 0$

Step 3

Set $c$ equal to $0$ .

$c = 0$

Step 4

Set $4 c + 3$ equal to $0$ and solve for $c$ .

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Step 4.1

Set $4 c + 3$ equal to $0$ .

$4 c + 3 = 0$

Step 4.2

Solve $4 c + 3 = 0$ for $c$ .

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$4 c = - 3$

Step 4.2.2

Divide each term in $4 c = - 3$ by $4$ and simplify.

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Step 4.2.2.1

Divide each term in $4 c = - 3$ by $4$ .

$\frac{4 c}{4} = \frac{- 3}{4}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{4 c}{4} = \frac{- 3}{4}$

Step 4.2.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{- 3}{4}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Move the negative in front of the fraction.

$c = - \frac{3}{4}$

Step 5

Set $4 c - 3$ equal to $0$ and solve for $c$ .

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Step 5.1

Set $4 c - 3$ equal to $0$ .

$4 c - 3 = 0$

Step 5.2

Solve $4 c - 3 = 0$ for $c$ .

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Step 5.2.1

Add $3$ to both sides of the equation.

$4 c = 3$

Step 5.2.2

Divide each term in $4 c = 3$ by $4$ and simplify.

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Step 5.2.2.1

Divide each term in $4 c = 3$ by $4$ .

$\frac{4 c}{4} = \frac{3}{4}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{4 c}{4} = \frac{3}{4}$

Step 5.2.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{3}{4}$

Step 6

The final solution is all the values that make $c (4 c + 3) (4 c - 3) = 0$ true.

$c = 0, - \frac{3}{4}, \frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$c = 0, - \frac{3}{4}, \frac{3}{4}$

Decimal Form:

$c = 0, - 0.75, 0.75$