Solve (x+6)^2-5x=4x^2+7x-12

$$( x + 6 ) ^ { 2 } - 5 x = 4 x ^ { 2 } + 7 x - 12$$

Solve for x

$$x=-4$$

$$x=4$$

Steps by Finding Square Root

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-5x=4x^{2}+7x-12$$

Combine 12x and -5x to get 7x.

$$x^{2}+7x+36=4x^{2}+7x-12$$

Subtract 4x^{2} from both sides.

$$x^{2}+7x+36-4x^{2}=7x-12$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+7x+36=7x-12$$

Subtract 7x from both sides.

$$-3x^{2}+7x+36-7x=-12$$

Combine 7x and -7x to get 0.

$$-3x^{2}+36=-12$$

Subtract 36 from both sides.

$$-3x^{2}=-12-36$$

Subtract 36 from -12 to get -48.

$$-3x^{2}=-48$$

Divide both sides by -3.

$$x^{2}=\frac{-48}{-3}$$

Divide -48 by -3 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-5x=4x^{2}+7x-12$$

Combine 12x and -5x to get 7x.

$$x^{2}+7x+36=4x^{2}+7x-12$$

Subtract 4x^{2} from both sides.

$$x^{2}+7x+36-4x^{2}=7x-12$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+7x+36=7x-12$$

Subtract 7x from both sides.

$$-3x^{2}+7x+36-7x=-12$$

Combine 7x and -7x to get 0.

$$-3x^{2}+36=-12$$

Add 12 to both sides.

$$-3x^{2}+36+12=0$$

Add 36 and 12 to get 48.

$$-3x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 48}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 48}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 48}}{2\left(-3\right)}$$

Multiply 12 times 48.

$$x=\frac{0±\sqrt{576}}{2\left(-3\right)}$$

Take the square root of 576.

$$x=\frac{0±24}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±24}{-6}$$

Now solve the equation x=\frac{0±24}{-6} when ± is plus. Divide 24 by -6.

$$x=-4$$

Now solve the equation x=\frac{0±24}{-6} when ± is minus. Divide -24 by -6.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$