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

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

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

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

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

Multiply (-9 + 2x) * (-9 + 2x)
(-9(-9 + 2x) + 2x * (-9 + 2x)) = 9
((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) = 9
((81 + -18x) + 2x * (-9 + 2x)) = 9
(81 + -18x + (-9 * 2x + 2x * 2x)) = 9
(81 + -18x + (-18x + 4x2)) = 9

Combine like terms: -18x + -18x = -36x
(81 + -36x + 4x2) = 9

Solving
81 + -36x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
81 + -9 + -36x + 4x2 = 9 + -9

Combine like terms: 81 + -9 = 72
72 + -36x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
72 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9x + x2) = 0

Factor a trinomial.
4((3 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {3, 6}