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

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


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

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

Reorder the terms:
-2x + 2x2 = -3x + 6x2

Solving
-2x + 2x2 = -3x + 6x2

Solving for variable 'x'.

Reorder the terms:
-2x + 3x + 2x2 + -6x2 = -3x + 6x2 + 3x + -6x2

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

Combine like terms: 2x2 + -6x2 = -4x2
1x + -4x2 = -3x + 6x2 + 3x + -6x2

Reorder the terms:
1x + -4x2 = -3x + 3x + 6x2 + -6x2

Combine like terms: -3x + 3x = 0
1x + -4x2 = 0 + 6x2 + -6x2
1x + -4x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -4x) = 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 '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 0.25}

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