6x(x-1)=4x+4

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Solution for 6x(x-1)=4x+4 equation: 


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

Reorder the terms:
6x(-1 + x) = 4x + 4
(-1 * 6x + x * 6x) = 4x + 4
(-6x + 6x2) = 4x + 4

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

Solving
-6x + 6x2 = 4 + 4x

Solving for variable 'x'.

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

Combine like terms: -6x + -4x = -10x
-4 + -10x + 6x2 = 4 + 4x + -4 + -4x

Reorder the terms:
-4 + -10x + 6x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
-4 + -10x + 6x2 = 0 + 4x + -4x
-4 + -10x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + -10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.3333333333, 2}

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