x(2-2x)=12x-6x-5x^2

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Solution for x(2-2x)=12x-6x-5x^2 equation: 


Simplifying
x(2 + -2x) = 12x + -6x + -5x2
(2 * x + -2x * x) = 12x + -6x + -5x2
(2x + -2x2) = 12x + -6x + -5x2

Combine like terms: 12x + -6x = 6x
2x + -2x2 = 6x + -5x2

Solving
2x + -2x2 = 6x + -5x2

Solving for variable 'x'.

Reorder the terms:
2x + -6x + -2x2 + 5x2 = 6x + -5x2 + -6x + 5x2

Combine like terms: 2x + -6x = -4x
-4x + -2x2 + 5x2 = 6x + -5x2 + -6x + 5x2

Combine like terms: -2x2 + 5x2 = 3x2
-4x + 3x2 = 6x + -5x2 + -6x + 5x2

Reorder the terms:
-4x + 3x2 = 6x + -6x + -5x2 + 5x2

Combine like terms: 6x + -6x = 0
-4x + 3x2 = 0 + -5x2 + 5x2
-4x + 3x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-4x + 3x2 = 0

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


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 '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.333333333}

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