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

Solution for 2(x+1)(x-1)-(2x+3)(x-2)=0 equation:

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

Reorder the terms:
2(1 + x)(x + -1) + -1(2x + 3)(x + -2) = 0

Reorder the terms:
2(1 + x)(-1 + x) + -1(2x + 3)(x + -2) = 0

Multiply (1 + x) * (-1 + x)
2(1(-1 + x) + x(-1 + x)) + -1(2x + 3)(x + -2) = 0
2((-1 * 1 + x * 1) + x(-1 + x)) + -1(2x + 3)(x + -2) = 0
2((-1 + 1x) + x(-1 + x)) + -1(2x + 3)(x + -2) = 0
2(-1 + 1x + (-1 * x + x * x)) + -1(2x + 3)(x + -2) = 0
2(-1 + 1x + (-1x + x2)) + -1(2x + 3)(x + -2) = 0

Combine like terms: 1x + -1x = 0
2(-1 + 0 + x2) + -1(2x + 3)(x + -2) = 0
2(-1 + x2) + -1(2x + 3)(x + -2) = 0
(-1 * 2 + x2 * 2) + -1(2x + 3)(x + -2) = 0
(-2 + 2x2) + -1(2x + 3)(x + -2) = 0

Reorder the terms:
-2 + 2x2 + -1(3 + 2x)(x + -2) = 0

Reorder the terms:
-2 + 2x2 + -1(3 + 2x)(-2 + x) = 0

Multiply (3 + 2x) * (-2 + x)
-2 + 2x2 + -1(3(-2 + x) + 2x * (-2 + x)) = 0
-2 + 2x2 + -1((-2 * 3 + x * 3) + 2x * (-2 + x)) = 0
-2 + 2x2 + -1((-6 + 3x) + 2x * (-2 + x)) = 0
-2 + 2x2 + -1(-6 + 3x + (-2 * 2x + x * 2x)) = 0
-2 + 2x2 + -1(-6 + 3x + (-4x + 2x2)) = 0

Combine like terms: 3x + -4x = -1x
-2 + 2x2 + -1(-6 + -1x + 2x2) = 0
-2 + 2x2 + (-6 * -1 + -1x * -1 + 2x2 * -1) = 0
-2 + 2x2 + (6 + 1x + -2x2) = 0

Reorder the terms:
-2 + 6 + 1x + 2x2 + -2x2 = 0

Combine like terms: -2 + 6 = 4
4 + 1x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
4 + 1x + 0 = 0
4 + 1x = 0

Solving
4 + 1x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 1x = 0 + -4
1x = 0 + -4

Combine like terms: 0 + -4 = -4
1x = -4

Divide each side by '1'.
x = -4

Simplifying
x = -4