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

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


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

Reorder the terms:
-6(-1 + x) * x = 2x + -1x + 3x

Reorder the terms for easier multiplication:
-6x(-1 + x) = 2x + -1x + 3x
(-1 * -6x + x * -6x) = 2x + -1x + 3x
(6x + -6x2) = 2x + -1x + 3x

Combine like terms: 2x + -1x = 1x
6x + -6x2 = 1x + 3x

Combine like terms: 1x + 3x = 4x
6x + -6x2 = 4x

Solving
6x + -6x2 = 4x

Solving for variable 'x'.

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

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

Combine like terms: 4x + -4x = 0
2x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -3x) = 0

Ignore the factor 2.

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 '(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
Solution
x = {0, 0.3333333333}

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