Solve (x-2)(x+3)(x-4)=(x+2)(x-3)(x+4)

$$( x - 2 ) ( x + 3 ) ( x - 4 ) = ( x + 2 ) ( x - 3 ) ( x + 4 )$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Use the distributive property to multiply x-2 by x+3 and combine like terms.

$$\left(x^{2}+x-6\right)\left(x-4\right)=\left(x+2\right)\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply x^{2}+x-6 by x-4 and combine like terms.

$$x^{3}-3x^{2}-10x+24=\left(x+2\right)\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$x^{3}-3x^{2}-10x+24=\left(x^{2}-x-6\right)\left(x+4\right)$$

Use the distributive property to multiply x^{2}-x-6 by x+4 and combine like terms.

$$x^{3}-3x^{2}-10x+24=x^{3}+3x^{2}-10x-24$$

Subtract x^{3} from both sides.

$$x^{3}-3x^{2}-10x+24-x^{3}=3x^{2}-10x-24$$

Combine x^{3} and -x^{3} to get 0.

$$-3x^{2}-10x+24=3x^{2}-10x-24$$

Subtract 3x^{2} from both sides.

$$-3x^{2}-10x+24-3x^{2}=-10x-24$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$-6x^{2}-10x+24=-10x-24$$

Add 10x to both sides.

$$-6x^{2}-10x+24+10x=-24$$

Combine -10x and 10x to get 0.

$$-6x^{2}+24=-24$$

Subtract 24 from both sides.

$$-6x^{2}=-24-24$$

Subtract 24 from -24 to get -48.

$$-6x^{2}=-48$$

Divide both sides by -6.

$$x^{2}=\frac{-48}{-6}$$

Divide -48 by -6 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

$$x=2\sqrt{2} x=-2\sqrt{2}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-2 by x+3 and combine like terms.

$$\left(x^{2}+x-6\right)\left(x-4\right)=\left(x+2\right)\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply x^{2}+x-6 by x-4 and combine like terms.

$$x^{3}-3x^{2}-10x+24=\left(x+2\right)\left(x-3\right)\left(x+4\right)$$

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$x^{3}-3x^{2}-10x+24=\left(x^{2}-x-6\right)\left(x+4\right)$$

Use the distributive property to multiply x^{2}-x-6 by x+4 and combine like terms.

$$x^{3}-3x^{2}-10x+24=x^{3}+3x^{2}-10x-24$$

Subtract x^{3} from both sides.

$$x^{3}-3x^{2}-10x+24-x^{3}=3x^{2}-10x-24$$

Combine x^{3} and -x^{3} to get 0.

$$-3x^{2}-10x+24=3x^{2}-10x-24$$

Subtract 3x^{2} from both sides.

$$-3x^{2}-10x+24-3x^{2}=-10x-24$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$-6x^{2}-10x+24=-10x-24$$

Add 10x to both sides.

$$-6x^{2}-10x+24+10x=-24$$

Combine -10x and 10x to get 0.

$$-6x^{2}+24=-24$$

Add 24 to both sides.

$$-6x^{2}+24+24=0$$

Add 24 and 24 to get 48.

$$-6x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 48}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 48}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 48}}{2\left(-6\right)}$$

Multiply 24 times 48.

$$x=\frac{0±\sqrt{1152}}{2\left(-6\right)}$$

Take the square root of 1152.

$$x=\frac{0±24\sqrt{2}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±24\sqrt{2}}{-12}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-12} when ± is plus.

$$x=-2\sqrt{2}$$

Now solve the equation x=\frac{0±24\sqrt{2}}{-12} when ± is minus.

$$x=2\sqrt{2}$$

The equation is now solved.

$$x=-2\sqrt{2} x=2\sqrt{2}$$