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

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

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

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

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

Solving
-6x + 2x2 = -6 + 2x

Solving for variable 'x'.

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

Combine like terms: -6x + -2x = -8x
6 + -8x + 2x2 = -6 + 2x + 6 + -2x

Reorder the terms:
6 + -8x + 2x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
6 + -8x + 2x2 = 0 + 2x + -2x
6 + -8x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4x + x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {1, 3}