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

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

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

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

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

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

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

Reorder the terms:
6 + -1x + -2x2 = (1 + x)(2x + -3)

Reorder the terms:
6 + -1x + -2x2 = (1 + x)(-3 + 2x)

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

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

Add 'x' to each side of the equation.
6 + -1x + x + -2x2 = -3 + -1x + x + 2x2

Combine like terms: -1x + x = 0
6 + 0 + -2x2 = -3 + -1x + x + 2x2
6 + -2x2 = -3 + -1x + x + 2x2

Combine like terms: -1x + x = 0
6 + -2x2 = -3 + 0 + 2x2
6 + -2x2 = -3 + 2x2

Solving
6 + -2x2 = -3 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
6 + -2x2 + -2x2 = -3 + 2x2 + -2x2

Combine like terms: -2x2 + -2x2 = -4x2
6 + -4x2 = -3 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -4x2 = -3 + 0
6 + -4x2 = -3

Add '-6' to each side of the equation.
6 + -6 + -4x2 = -3 + -6

Combine like terms: 6 + -6 = 0
0 + -4x2 = -3 + -6
-4x2 = -3 + -6

Combine like terms: -3 + -6 = -9
-4x2 = -9

Divide each side by '-4'.
x2 = 2.25

Simplifying
x2 = 2.25

Take the square root of each side:
x = {-1.5, 1.5}