Solve (x+2)(x+1)(x-2)=x^3+3x^2-4

$$( x + 2 ) ( x + 1 ) ( x - 2 ) = x ^ { 3 } + 3 x ^ { 2 } - 4$$

Solve for x

$$x=-2$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply x+2 by x+1 and combine like terms.

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

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

$$x^{3}+x^{2}-4x-4=x^{3}+3x^{2}-4$$

Subtract x^{3} from both sides.

$$x^{3}+x^{2}-4x-4-x^{3}=3x^{2}-4$$

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

$$x^{2}-4x-4=3x^{2}-4$$

Subtract 3x^{2} from both sides.

$$x^{2}-4x-4-3x^{2}=-4$$

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

$$-2x^{2}-4x-4=-4$$

Add 4 to both sides.

$$-2x^{2}-4x-4+4=0$$

Add -4 and 4 to get 0.

$$-2x^{2}-4x=0$$

Factor out x.

$$x\left(-2x-4\right)=0$$

To find equation solutions, solve x=0 and -2x-4=0.

$$x=0 x=-2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+2 by x+1 and combine like terms.

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

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

$$x^{3}+x^{2}-4x-4=x^{3}+3x^{2}-4$$

Subtract x^{3} from both sides.

$$x^{3}+x^{2}-4x-4-x^{3}=3x^{2}-4$$

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

$$x^{2}-4x-4=3x^{2}-4$$

Subtract 3x^{2} from both sides.

$$x^{2}-4x-4-3x^{2}=-4$$

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

$$-2x^{2}-4x-4=-4$$

Add 4 to both sides.

$$-2x^{2}-4x-4+4=0$$

Add -4 and 4 to get 0.

$$-2x^{2}-4x=0$$

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

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

Take the square root of \left(-4\right)^{2}.

$$x=\frac{-\left(-4\right)±4}{2\left(-2\right)}$$

The opposite of -4 is 4.

$$x=\frac{4±4}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{4±4}{-4}$$

Now solve the equation x=\frac{4±4}{-4} when ± is plus. Add 4 to 4.

$$x=\frac{8}{-4}$$

Divide 8 by -4.

$$x=-2$$

Now solve the equation x=\frac{4±4}{-4} when ± is minus. Subtract 4 from 4.

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

The equation is now solved.

$$x=-2 x=0$$

Steps for Completing the Square

Use the distributive property to multiply x+2 by x+1 and combine like terms.

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

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

$$x^{3}+x^{2}-4x-4=x^{3}+3x^{2}-4$$

Subtract x^{3} from both sides.

$$x^{3}+x^{2}-4x-4-x^{3}=3x^{2}-4$$

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

$$x^{2}-4x-4=3x^{2}-4$$

Subtract 3x^{2} from both sides.

$$x^{2}-4x-4-3x^{2}=-4$$

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

$$-2x^{2}-4x-4=-4$$

Add 4 to both sides.

$$-2x^{2}-4x=-4+4$$

Add -4 and 4 to get 0.

$$-2x^{2}-4x=0$$

Divide both sides by -2.

$$\frac{-2x^{2}-4x}{-2}=\frac{0}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\left(-\frac{4}{-2}\right)x=\frac{0}{-2}$$

Divide -4 by -2.

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

Divide 0 by -2.

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

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=1^{2}$$

Square 1.

$$x^{2}+2x+1=1$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{1}$$

Simplify.

$$x+1=1 x+1=-1$$

Subtract 1 from both sides of the equation.

$$x=0 x=-2$$