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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-1 = -6 + 1x

Solving for variable 'x'.

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

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

Combine like terms: 1x + -1x = 0
-1 + -1x = -6 + 0
-1 + -1x = -6

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

Combine like terms: -1 + 1 = 0
0 + -1x = -6 + 1
-1x = -6 + 1

Combine like terms: -6 + 1 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5