Algebra Examples

$f (x) = (x - 6) (2 x + 10)$

Step 1

Set $(x - 6) (2 x + 10)$ equal to $0$ .

$(x - 6) (2 x + 10) = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$x - 6 = 0$

$2 x + 10 = 0$

Step 2.2

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 2.2.2

Add $6$ to both sides of the equation.

$x = 6$

Step 2.3

Set $2 x + 10$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $2 x + 10$ equal to $0$ .

$2 x + 10 = 0$

Step 2.3.2

Solve $2 x + 10 = 0$ for $x$ .

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Step 2.3.2.1

Subtract $10$ from both sides of the equation.

$2 x = - 10$

Step 2.3.2.2

Divide each term in $2 x = - 10$ by $2$ and simplify.

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Step 2.3.2.2.1

Divide each term in $2 x = - 10$ by $2$ .

$\frac{2 x}{2} = \frac{- 10}{2}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10}{2}$

Step 2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{2}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Divide $- 10$ by $2$ .

$x = - 5$

Step 2.4

The final solution is all the values that make $(x - 6) (2 x + 10) = 0$ true.

$x = 6, - 5$

Step 3