(2x-1)(2x-1)=9

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Solution for (2x-1)(2x-1)=9 equation: 


Simplifying
(2x + -1)(2x + -1) = 9

Reorder the terms:
(-1 + 2x)(2x + -1) = 9

Reorder the terms:
(-1 + 2x)(-1 + 2x) = 9

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) = 9
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 9
((1 + -2x) + 2x * (-1 + 2x)) = 9
(1 + -2x + (-1 * 2x + 2x * 2x)) = 9
(1 + -2x + (-2x + 4x2)) = 9

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) = 9

Solving
1 + -4x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
1 + -9 + -4x + 4x2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + -4x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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