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

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

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

Reorder the terms:
x(-3 + x) + -2(x + -3) = 6
(-3 * x + x * x) + -2(x + -3) = 6
(-3x + x2) + -2(x + -3) = 6

Reorder the terms:
-3x + x2 + -2(-3 + x) = 6
-3x + x2 + (-3 * -2 + x * -2) = 6
-3x + x2 + (6 + -2x) = 6

Reorder the terms:
6 + -3x + -2x + x2 = 6

Combine like terms: -3x + -2x = -5x
6 + -5x + x2 = 6

Add '-6' to each side of the equation.
6 + -5x + -6 + x2 = 6 + -6

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

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

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

Solving
-5x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, 5}