3(x-4)-x=2x(x-6)

Solution for 3(x-4)-x=2x(x-6) equation:

Simplifying
3(x + -4) + -1x = 2x(x + -6)

Reorder the terms:
3(-4 + x) + -1x = 2x(x + -6)
(-4 * 3 + x * 3) + -1x = 2x(x + -6)
(-12 + 3x) + -1x = 2x(x + -6)

Combine like terms: 3x + -1x = 2x
-12 + 2x = 2x(x + -6)

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

Solving
-12 + 2x = -12x + 2x2

Solving for variable 'x'.

Combine like terms: 2x + 12x = 14x
-12 + 14x + -2x2 = -12x + 2x2 + 12x + -2x2

Reorder the terms:
-12 + 14x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-12 + 14x + -2x2 = 0 + 2x2 + -2x2
-12 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {6, 1}