2x(4x-1)=x(1-4x)

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Solution for 2x(4x-1)=x(1-4x) equation: 


Simplifying
2x(4x + -1) = x(1 + -4x)

Reorder the terms:
2x(-1 + 4x) = x(1 + -4x)
(-1 * 2x + 4x * 2x) = x(1 + -4x)
(-2x + 8x2) = x(1 + -4x)
-2x + 8x2 = (1 * x + -4x * x)
-2x + 8x2 = (1x + -4x2)

Solving
-2x + 8x2 = 1x + -4x2

Solving for variable 'x'.

Reorder the terms:
-2x + -1x + 8x2 + 4x2 = 1x + -4x2 + -1x + 4x2

Combine like terms: -2x + -1x = -3x
-3x + 8x2 + 4x2 = 1x + -4x2 + -1x + 4x2

Combine like terms: 8x2 + 4x2 = 12x2
-3x + 12x2 = 1x + -4x2 + -1x + 4x2

Reorder the terms:
-3x + 12x2 = 1x + -1x + -4x2 + 4x2

Combine like terms: 1x + -1x = 0
-3x + 12x2 = 0 + -4x2 + 4x2
-3x + 12x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + 4x) = 0

Ignore the factor 3.

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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