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

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


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

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

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

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

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

Solving
16 + -16x + 4x2 = 1

Solving for variable 'x'.

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

Combine like terms: 16 + -1 = 15
15 + -16x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
15 + -16x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.5, 2.5}

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