Solve (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0

$$( x + 2 ) ( x + 3 ) + ( x - 3 ) ( x - 2 ) - 2 x ( x + 1 ) = 0$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$x^{2}+5x+6+\left(x-3\right)\left(x-2\right)-2x\left(x+1\right)=0$$

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

$$x^{2}+5x+6+x^{2}-5x+6-2x\left(x+1\right)=0$$

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

$$2x^{2}+5x+6-5x+6-2x\left(x+1\right)=0$$

Combine 5x and -5x to get 0.

$$2x^{2}+6+6-2x\left(x+1\right)=0$$

Add 6 and 6 to get 12.

$$2x^{2}+12-2x\left(x+1\right)=0$$

Use the distributive property to multiply -2x by x+1.

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

Combine 2x^{2} and -2x^{2} to get 0.

$$12-2x=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-12$$

Divide both sides by -2.

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

Divide -12 by -2 to get 6.

$$x=6$$