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

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

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

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

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

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

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

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

Remove parenthesis around (-3 + x)
-6 + -1x + x2 = -3 + x

Solving
-6 + -1x + x2 = -3 + x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}