Solve by Factoring x^2+12x=x-24

$x^{2} + 12 x = x - 24$

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} + 12 x - x = - 24$

Add $24$ to both sides of the equation.

$x^{2} + 12 x - x + 24 = 0$

Step 2

Subtract $x$ from $12 x$ .

$x^{2} + 11 x + 24 = 0$

Step 3

Factor $x^{2} + 11 x + 24$ using the AC method.

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 $24$ and whose sum is $11$ .

$3, 8$

Write the factored form using these integers.

$(x + 3) (x + 8) = 0$

Step 4

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

$x + 3 = 0$

$x + 8 = 0$

Step 5

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

Set $x + 8$ equal to $0$ and solve for $x$ .

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 7

The final solution is all the values that make $(x + 3) (x + 8) = 0$ true.

$x = - 3, - 8$

Solve by Factoring x^2+12x=x-24

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