Solve for x -3x^2=12x+12

$- 3 x^{2} = 12 x + 12$

Subtract $12 x$ from both sides of the equation.

$- 3 x^{2} - 12 x = 12$

Subtract $12$ from both sides of the equation.

$- 3 x^{2} - 12 x - 12 = 0$

Factor the left side of the equation.

Factor $- 3$ out of $- 3 x^{2} - 12 x - 12$ .

Factor $- 3$ out of $- 3 x^{2}$ .

$- 3 x^{2} - 12 x - 12 = 0$

Factor $- 3$ out of $- 12 x$ .

$- 3 x^{2} - 3 (4 x) - 12 = 0$

Factor $- 3$ out of $- 12$ .

$- 3 x^{2} - 3 (4 x) - 3 \cdot 4 = 0$

Factor $- 3$ out of $- 3 (x^{2}) - 3 (4 x)$ .

$- 3 (x^{2} + 4 x) - 3 \cdot 4 = 0$

Factor $- 3$ out of $- 3 (x^{2} + 4 x) - 3 (4)$ .

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

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

$- 3 (x^{2} + 2 \cdot x \cdot 2 + 2^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 2$ .

$- 3 {(x + 2)}^{2} = 0$

Divide each term in $- 3 {(x + 2)}^{2} = 0$ by $- 3$ and simplify.

Divide each term in $- 3 {(x + 2)}^{2} = 0$ by $- 3$ .

$\frac{- 3 {(x + 2)}^{2}}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 {(x + 2)}^{2}}{- 3} = \frac{0}{- 3}$

Divide ${(x + 2)}^{2}$ by $1$ .

${(x + 2)}^{2} = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

${(x + 2)}^{2} = 0$

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$