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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -4x + -2x = -6x
1 + -6x + 8x2 = -1 + 2x + 1 + -2x

Reorder the terms:
1 + -6x + 8x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
1 + -6x + 8x2 = 0 + 2x + -2x
1 + -6x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
1 + -6x + 8x2 = 0

Factor a trinomial.
(1 + -4x)(1 + -2x) = 0


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.25, 0.5}

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