3(2x-6)(x-6)=60

Solution for 3(2x-6)(x-6)=60 equation:

Simplifying
3(2x + -6)(x + -6) = 60

Reorder the terms:
3(-6 + 2x)(x + -6) = 60

Reorder the terms:
3(-6 + 2x)(-6 + x) = 60

Multiply (-6 + 2x) * (-6 + x)
3(-6(-6 + x) + 2x * (-6 + x)) = 60
3((-6 * -6 + x * -6) + 2x * (-6 + x)) = 60
3((36 + -6x) + 2x * (-6 + x)) = 60
3(36 + -6x + (-6 * 2x + x * 2x)) = 60
3(36 + -6x + (-12x + 2x2)) = 60

Combine like terms: -6x + -12x = -18x
3(36 + -18x + 2x2) = 60
(36 * 3 + -18x * 3 + 2x2 * 3) = 60
(108 + -54x + 6x2) = 60

Solving
108 + -54x + 6x2 = 60

Solving for variable 'x'.

Reorder the terms:
108 + -60 + -54x + 6x2 = 60 + -60

Combine like terms: 108 + -60 = 48
48 + -54x + 6x2 = 60 + -60

Combine like terms: 60 + -60 = 0
48 + -54x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -9x + x2) = 0

Factor a trinomial.
6((1 + -1x)(8 + -1x)) = 0

Ignore the factor 6.
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 '(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
Solution
x = {1, 8}