3(x-5)2(x-1)=8

Solution for 3(x-5)2(x-1)=8 equation:

Simplifying
3(x + -5) * 2(x + -1) = 8

Reorder the terms:
3(-5 + x) * 2(x + -1) = 8

Reorder the terms:
3(-5 + x) * 2(-1 + x) = 8

Reorder the terms for easier multiplication:
3 * 2(-5 + x)(-1 + x) = 8

Multiply 3 * 2
6(-5 + x)(-1 + x) = 8

Multiply (-5 + x) * (-1 + x)
6(-5(-1 + x) + x(-1 + x)) = 8
6((-1 * -5 + x * -5) + x(-1 + x)) = 8
6((5 + -5x) + x(-1 + x)) = 8
6(5 + -5x + (-1 * x + x * x)) = 8
6(5 + -5x + (-1x + x2)) = 8

Combine like terms: -5x + -1x = -6x
6(5 + -6x + x2) = 8
(5 * 6 + -6x * 6 + x2 * 6) = 8
(30 + -36x + 6x2) = 8

Solving
30 + -36x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
30 + -8 + -36x + 6x2 = 8 + -8

Combine like terms: 30 + -8 = 22
22 + -36x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
22 + -36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -18x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
11 + -18x + 3x2 = 0

Solving
11 + -18x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -6x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -6x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -3.666666667
-6x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-6x + x2 = -3.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -3.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -3.666666667 + 9

Combine like terms: -3.666666667 + 9 = 5.333333333
9 + -6x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + -3) equal to 2.309401077 and -2.309401077.

Subproblem 1
x + -3 = 2.309401077

Simplifying
x + -3 = 2.309401077

Reorder the terms:
-3 + x = 2.309401077

Solving
-3 + x = 2.309401077

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.309401077 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.309401077 + 3
x = 2.309401077 + 3

Combine like terms: 2.309401077 + 3 = 5.309401077
x = 5.309401077

Simplifying
x = 5.309401077

Subproblem 2
x + -3 = -2.309401077

Simplifying
x + -3 = -2.309401077

Reorder the terms:
-3 + x = -2.309401077

Solving
-3 + x = -2.309401077

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.309401077 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.309401077 + 3
x = -2.309401077 + 3

Combine like terms: -2.309401077 + 3 = 0.690598923
x = 0.690598923

Simplifying
x = 0.690598923

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.309401077, 0.690598923}
Solution
x = {5.309401077, 0.690598923}