Solve (2x-3)(3x+2)-(2x+3)(2-3x)=0

$$( 2 x - 3 ) ( 3 x + 2 ) - ( 2 x + 3 ) ( 2 - 3 x ) = 0$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using Difference of Squares

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

$$6x^{2}-5x-6-\left(2x+3\right)\left(2-3x\right)=0$$

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

$$6x^{2}-5x-6-\left(-5x-6x^{2}+6\right)=0$$

To find the opposite of -5x-6x^{2}+6, find the opposite of each term.

$$6x^{2}-5x-6+5x+6x^{2}-6=0$$

Combine -5x and 5x to get 0.

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

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-6-6=0$$

Subtract 6 from -6 to get -12.

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

Divide both sides by 12.

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

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

$$6x^{2}-5x-6-\left(2x+3\right)\left(2-3x\right)=0$$

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

$$6x^{2}-5x-6-\left(-5x-6x^{2}+6\right)=0$$

To find the opposite of -5x-6x^{2}+6, find the opposite of each term.

$$6x^{2}-5x-6+5x+6x^{2}-6=0$$

Combine -5x and 5x to get 0.

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

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-6-6=0$$

Subtract 6 from -6 to get -12.

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

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

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

Divide both sides by 12.

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

Divide 12 by 12 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

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

$$6x^{2}-5x-6-\left(2x+3\right)\left(2-3x\right)=0$$

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

$$6x^{2}-5x-6-\left(-5x-6x^{2}+6\right)=0$$

To find the opposite of -5x-6x^{2}+6, find the opposite of each term.

$$6x^{2}-5x-6+5x+6x^{2}-6=0$$

Combine -5x and 5x to get 0.

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

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-6-6=0$$

Subtract 6 from -6 to get -12.

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

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

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

Square 0.

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

Multiply -4 times 12.

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

Multiply -48 times -12.

$$x=\frac{0±\sqrt{576}}{2\times 12}$$

Take the square root of 576.

$$x=\frac{0±24}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±24}{24}$$

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

$$x=1$$

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

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$