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

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

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

Reorder the terms:
2(-2 + x) = (x + -2)(x + 3)
(-2 * 2 + x * 2) = (x + -2)(x + 3)
(-4 + 2x) = (x + -2)(x + 3)

Reorder the terms:
-4 + 2x = (-2 + x)(x + 3)

Reorder the terms:
-4 + 2x = (-2 + x)(3 + x)

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

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

Solving
-4 + 2x = -6 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + 2x + -1x + -1x2 = -6 + 1x + x2 + 6 + -1x + -1x2

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

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

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

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

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

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

Factor a trinomial.
(2 + -1x)(1 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {2, -1}