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

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


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

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

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

Multiply (-2 + 4x) * (-2 + 4x)
(-2(-2 + 4x) + 4x * (-2 + 4x)) = 1
((-2 * -2 + 4x * -2) + 4x * (-2 + 4x)) = 1
((4 + -8x) + 4x * (-2 + 4x)) = 1
(4 + -8x + (-2 * 4x + 4x * 4x)) = 1
(4 + -8x + (-8x + 16x2)) = 1

Combine like terms: -8x + -8x = -16x
(4 + -16x + 16x2) = 1

Solving
4 + -16x + 16x2 = 1

Solving for variable 'x'.

Reorder the terms:
4 + -1 + -16x + 16x2 = 1 + -1

Combine like terms: 4 + -1 = 3
3 + -16x + 16x2 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + -16x + 16x2 = 0

Factor a trinomial.
(1 + -4x)(3 + -4x) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0.25, 0.75}

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