3x(2-2x)=-6(x-1)

Solution for 3x(2-2x)=-6(x-1) equation:

Simplifying
3x(2 + -2x) = -6(x + -1)
(2 * 3x + -2x * 3x) = -6(x + -1)
(6x + -6x2) = -6(x + -1)

Reorder the terms:
6x + -6x2 = -6(-1 + x)
6x + -6x2 = (-1 * -6 + x * -6)
6x + -6x2 = (6 + -6x)

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

Solving for variable 'x'.

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

Combine like terms: 6x + 6x = 12x
-6 + 12x + -6x2 = 6 + -6x + -6 + 6x

Reorder the terms:
-6 + 12x + -6x2 = 6 + -6 + -6x + 6x

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

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

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

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

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
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 = {1, 1}