Solve x(x+3)-12=x(3-x)

$$x ( x + 3 ) - 12 = x ( 3 - x )$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Use the distributive property to multiply x by x+3.

$$x^{2}+3x-12=x\left(3-x\right)$$

Use the distributive property to multiply x by 3-x.

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

Subtract 3x from both sides.

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

Combine 3x and -3x to get 0.

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Add 12 to both sides. Anything plus zero gives itself.

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

Divide both sides by 2.

$$x^{2}=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+3.

$$x^{2}+3x-12=x\left(3-x\right)$$

Use the distributive property to multiply x by 3-x.

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

Subtract 3x from both sides.

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

Combine 3x and -3x to get 0.

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-12\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-12\right)}}{2\times 2}$$

Multiply -8 times -12.

$$x=\frac{0±\sqrt{96}}{2\times 2}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{4} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{4} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$