3(x-6)(x-8)=90

Solution for 3(x-6)(x-8)=90 equation:

Simplifying
3(x + -6)(x + -8) = 90

Reorder the terms:
3(-6 + x)(x + -8) = 90

Reorder the terms:
3(-6 + x)(-8 + x) = 90

Multiply (-6 + x) * (-8 + x)
3(-6(-8 + x) + x(-8 + x)) = 90
3((-8 * -6 + x * -6) + x(-8 + x)) = 90
3((48 + -6x) + x(-8 + x)) = 90
3(48 + -6x + (-8 * x + x * x)) = 90
3(48 + -6x + (-8x + x2)) = 90

Combine like terms: -6x + -8x = -14x
3(48 + -14x + x2) = 90
(48 * 3 + -14x * 3 + x2 * 3) = 90
(144 + -42x + 3x2) = 90

Solving
144 + -42x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
144 + -90 + -42x + 3x2 = 90 + -90

Combine like terms: 144 + -90 = 54
54 + -42x + 3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
54 + -42x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -14x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(18 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -14x + x2 = 0

Solving
18 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -14x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -14x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -14x + x2 = 0 + -18
-14x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-14x + x2 = -18

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -18 + 49

Reorder the terms:
49 + -14x + x2 = -18 + 49

Combine like terms: -18 + 49 = 31
49 + -14x + x2 = 31

Factor a perfect square on the left side:
(x + -7)(x + -7) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -7) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + -7 = 5.567764363

Simplifying
x + -7 = 5.567764363

Reorder the terms:
-7 + x = 5.567764363

Solving
-7 + x = 5.567764363

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.567764363 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.567764363 + 7
x = 5.567764363 + 7

Combine like terms: 5.567764363 + 7 = 12.567764363
x = 12.567764363

Simplifying
x = 12.567764363

Subproblem 2
x + -7 = -5.567764363

Simplifying
x + -7 = -5.567764363

Reorder the terms:
-7 + x = -5.567764363

Solving
-7 + x = -5.567764363

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.567764363 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.567764363 + 7
x = -5.567764363 + 7

Combine like terms: -5.567764363 + 7 = 1.432235637
x = 1.432235637

Simplifying
x = 1.432235637

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.567764363, 1.432235637}
Solution
x = {12.567764363, 1.432235637}