12(x-3)-2x(x-3)=0

Solution for 12(x-3)-2x(x-3)=0 equation:

Simplifying
12(x + -3) + -2x(x + -3) = 0

Reorder the terms:
12(-3 + x) + -2x(x + -3) = 0
(-3 * 12 + x * 12) + -2x(x + -3) = 0
(-36 + 12x) + -2x(x + -3) = 0

Reorder the terms:
-36 + 12x + -2x(-3 + x) = 0
-36 + 12x + (-3 * -2x + x * -2x) = 0
-36 + 12x + (6x + -2x2) = 0

Combine like terms: 12x + 6x = 18x
-36 + 18x + -2x2 = 0

Solving
-36 + 18x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

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

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 3}