(2x-3)(2x-3)=1

Solution for (2x-3)(2x-3)=1 equation:

Simplifying
(2x + -3)(2x + -3) = 1

Reorder the terms:
(-3 + 2x)(2x + -3) = 1

Reorder the terms:
(-3 + 2x)(-3 + 2x) = 1

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) = 1
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 1
((9 + -6x) + 2x * (-3 + 2x)) = 1
(9 + -6x + (-3 * 2x + 2x * 2x)) = 1
(9 + -6x + (-6x + 4x2)) = 1

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) = 1

Solving
9 + -12x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
9 + -1 + -12x + 4x2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + -12x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -3x + 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}