2x(x-1)=4(3x-3)

Solution for 2x(x-1)=4(3x-3) equation:

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

Reorder the terms:
2x(-1 + x) = 4(3x + -3)
(-1 * 2x + x * 2x) = 4(3x + -3)
(-2x + 2x2) = 4(3x + -3)

Reorder the terms:
-2x + 2x2 = 4(-3 + 3x)
-2x + 2x2 = (-3 * 4 + 3x * 4)
-2x + 2x2 = (-12 + 12x)

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
6 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 6

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