Algebra Examples

$g (x) = x (x + 8) + 12$

Step 1

Set $x (x + 8) + 12$ equal to $0$ .

$x (x + 8) + 12 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x \cdot x + x \cdot 8 + 12 = 0$

Step 2.1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 + 12 = 0$

Step 2.1.3

Move $8$ to the left of $x$ .

$x^{2} + 8 x + 12 = 0$

Step 2.2

Factor $x^{2} + 8 x + 12$ using the AC method.

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Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $12$ and whose sum is $8$ .

$2, 6$

Step 2.2.2

Write the factored form using these integers.

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

Step 2.3

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

$x + 2 = 0$

$x + 6 = 0$

Step 2.4

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

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Step 2.4.1

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

$x + 2 = 0$

Step 2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.5

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

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Step 2.5.1

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

$x + 6 = 0$

Step 2.5.2

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 2.6

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

$x = - 2, - 6$

Step 3