12x-2x^2-6xy=0

Solution for 12x-2x^2-6xy=0 equation:

Simplifying
12x + -2x2 + -6xy = 0

Reorder the terms:
12x + -6xy + -2x2 = 0

Solving
12x + -6xy + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + -3y + -1x) = 0

Ignore the factor 2.
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 '(6 + -3y + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -3y + -1x = 0

Reorder the terms:
6 + -1x + -3y = 0

Solving
6 + -1x + -3y = 0

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

Add '-6' to each side of the equation.
6 + -1x + -6 + -3y = 0 + -6

Reorder the terms:
6 + -6 + -1x + -3y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x + -3y = 0 + -6
-1x + -3y = 0 + -6

Combine like terms: 0 + -6 = -6
-1x + -3y = -6

Add '3y' to each side of the equation.
-1x + -3y + 3y = -6 + 3y

Combine like terms: -3y + 3y = 0
-1x + 0 = -6 + 3y
-1x = -6 + 3y

Divide each side by '-1'.
x = 6 + -3y

Simplifying
x = 6 + -3y
Solution
x = {0, 6 + -3y}