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

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

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

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

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

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

Combine like terms: -3x + 2x = -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