(x-6)(2x-6)=308

Solution for (x-6)(2x-6)=308 equation:

Simplifying
(x + -6)(2x + -6) = 308

Reorder the terms:
(-6 + x)(2x + -6) = 308

Reorder the terms:
(-6 + x)(-6 + 2x) = 308

Multiply (-6 + x) * (-6 + 2x)
(-6(-6 + 2x) + x(-6 + 2x)) = 308
((-6 * -6 + 2x * -6) + x(-6 + 2x)) = 308
((36 + -12x) + x(-6 + 2x)) = 308
(36 + -12x + (-6 * x + 2x * x)) = 308
(36 + -12x + (-6x + 2x2)) = 308

Combine like terms: -12x + -6x = -18x
(36 + -18x + 2x2) = 308

Solving
36 + -18x + 2x2 = 308

Solving for variable 'x'.

Reorder the terms:
36 + -308 + -18x + 2x2 = 308 + -308

Combine like terms: 36 + -308 = -272
-272 + -18x + 2x2 = 308 + -308

Combine like terms: 308 + -308 = 0
-272 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-136 + -9x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(17 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-8, 17}