(x+3)(x-2)=6(x-2)

Solution for (x+3)(x-2)=6(x-2) equation:

Simplifying
(x + 3)(x + -2) = 6(x + -2)

Reorder the terms:
(3 + x)(x + -2) = 6(x + -2)

Reorder the terms:
(3 + x)(-2 + x) = 6(x + -2)

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

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

Reorder the terms:
-6 + 1x + x2 = 6(-2 + x)
-6 + 1x + x2 = (-2 * 6 + x * 6)
-6 + 1x + x2 = (-12 + 6x)

Solving
-6 + 1x + x2 = -12 + 6x

Solving for variable 'x'.

Reorder the terms:
-6 + 12 + 1x + -6x + x2 = -12 + 6x + 12 + -6x

Combine like terms: -6 + 12 = 6
6 + 1x + -6x + x2 = -12 + 6x + 12 + -6x

Combine like terms: 1x + -6x = -5x
6 + -5x + x2 = -12 + 6x + 12 + -6x

Reorder the terms:
6 + -5x + x2 = -12 + 12 + 6x + -6x

Combine like terms: -12 + 12 = 0
6 + -5x + x2 = 0 + 6x + -6x
6 + -5x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
6 + -5x + x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -1x) = 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 '(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 = {2, 3}