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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-6 + 1x = -1

Solving for variable 'x'.

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

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

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

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

Divide each side by '1'.
x = 5

Simplifying
x = 5