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

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

Solve for x

$$x=-4$$

$$x=0$$

Steps Using the Quadratic Formula

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

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

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

$$x^{2}-x-6=3x^{2}+7x-6$$

Subtract 3x^{2} from both sides.

$$x^{2}-x-6-3x^{2}=7x-6$$

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

$$-2x^{2}-x-6=7x-6$$

Subtract 7x from both sides.

$$-2x^{2}-x-6-7x=-6$$

Combine -x and -7x to get -8x.

$$-2x^{2}-8x-6=-6$$

Add 6 to both sides.

$$-2x^{2}-8x-6+6=0$$

Add -6 and 6 to get 0.

$$-2x^{2}-8x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Take the square root of \left(-8\right)^{2}.

$$x=\frac{-\left(-8\right)±8}{2\left(-2\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±8}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{8±8}{-4}$$

Now solve the equation x=\frac{8±8}{-4} when ± is plus. Add 8 to 8.

$$x=\frac{16}{-4}$$

Divide 16 by -4.

$$x=-4$$

Now solve the equation x=\frac{8±8}{-4} when ± is minus. Subtract 8 from 8.

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

Divide 0 by -4.

$$x=0$$

The equation is now solved.

$$x=-4 x=0$$

Steps for Completing the Square

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

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

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

$$x^{2}-x-6=3x^{2}+7x-6$$

Subtract 3x^{2} from both sides.

$$x^{2}-x-6-3x^{2}=7x-6$$

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

$$-2x^{2}-x-6=7x-6$$

Subtract 7x from both sides.

$$-2x^{2}-x-6-7x=-6$$

Combine -x and -7x to get -8x.

$$-2x^{2}-8x-6=-6$$

Add 6 to both sides.

$$-2x^{2}-8x=-6+6$$

Add -6 and 6 to get 0.

$$-2x^{2}-8x=0$$

Divide both sides by -2.

$$\frac{-2x^{2}-8x}{-2}=\frac{0}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\left(-\frac{8}{-2}\right)x=\frac{0}{-2}$$

Divide -8 by -2.

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

Divide 0 by -2.

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

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 2.

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

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+2=2 x+2=-2$$

Subtract 2 from both sides of the equation.

$$x=0 x=-4$$