2(2x-1)(4x-1)=0

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Solution for 2(2x-1)(4x-1)=0 equation: 


Simplifying
2(2x + -1)(4x + -1) = 0

Reorder the terms:
2(-1 + 2x)(4x + -1) = 0

Reorder the terms:
2(-1 + 2x)(-1 + 4x) = 0

Multiply (-1 + 2x) * (-1 + 4x)
2(-1(-1 + 4x) + 2x * (-1 + 4x)) = 0
2((-1 * -1 + 4x * -1) + 2x * (-1 + 4x)) = 0
2((1 + -4x) + 2x * (-1 + 4x)) = 0
2(1 + -4x + (-1 * 2x + 4x * 2x)) = 0
2(1 + -4x + (-2x + 8x2)) = 0

Combine like terms: -4x + -2x = -6x
2(1 + -6x + 8x2) = 0
(1 * 2 + -6x * 2 + 8x2 * 2) = 0
(2 + -12x + 16x2) = 0

Solving
2 + -12x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + 8x2) = 0

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

Ignore the factor 2.

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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