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

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


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

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

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

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

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) = 4

Solving
1 + -4x + 4x2 = 4

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-1 + -2x)(3 + -2x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.5, 1.5}

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