2(x-6)(x-6)+5=23

Solution for 2(x-6)(x-6)+5=23 equation:

Simplifying
2(x + -6)(x + -6) + 5 = 23

Reorder the terms:
2(-6 + x)(x + -6) + 5 = 23

Reorder the terms:
2(-6 + x)(-6 + x) + 5 = 23

Multiply (-6 + x) * (-6 + x)
2(-6(-6 + x) + x(-6 + x)) + 5 = 23
2((-6 * -6 + x * -6) + x(-6 + x)) + 5 = 23
2((36 + -6x) + x(-6 + x)) + 5 = 23
2(36 + -6x + (-6 * x + x * x)) + 5 = 23
2(36 + -6x + (-6x + x2)) + 5 = 23

Combine like terms: -6x + -6x = -12x
2(36 + -12x + x2) + 5 = 23
(36 * 2 + -12x * 2 + x2 * 2) + 5 = 23
(72 + -24x + 2x2) + 5 = 23

Reorder the terms:
72 + 5 + -24x + 2x2 = 23

Combine like terms: 72 + 5 = 77
77 + -24x + 2x2 = 23

Solving
77 + -24x + 2x2 = 23

Solving for variable 'x'.

Reorder the terms:
77 + -23 + -24x + 2x2 = 23 + -23

Combine like terms: 77 + -23 = 54
54 + -24x + 2x2 = 23 + -23

Combine like terms: 23 + -23 = 0
54 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -12x + x2) = 0

Factor a trinomial.
2((3 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}