3(x-4)6x=8-3(x-5)

Solution for 3(x-4)6x=8-3(x-5) equation:

Simplifying
3(x + -4) * 6x = 8 + -3(x + -5)

Reorder the terms:
3(-4 + x) * 6x = 8 + -3(x + -5)

Reorder the terms for easier multiplication:
3 * 6x(-4 + x) = 8 + -3(x + -5)

Multiply 3 * 6
18x(-4 + x) = 8 + -3(x + -5)
(-4 * 18x + x * 18x) = 8 + -3(x + -5)
(-72x + 18x2) = 8 + -3(x + -5)

Reorder the terms:
-72x + 18x2 = 8 + -3(-5 + x)
-72x + 18x2 = 8 + (-5 * -3 + x * -3)
-72x + 18x2 = 8 + (15 + -3x)

Combine like terms: 8 + 15 = 23
-72x + 18x2 = 23 + -3x

Solving
-72x + 18x2 = 23 + -3x

Solving for variable 'x'.

Reorder the terms:
-23 + -72x + 3x + 18x2 = 23 + -3x + -23 + 3x

Combine like terms: -72x + 3x = -69x
-23 + -69x + 18x2 = 23 + -3x + -23 + 3x

Reorder the terms:
-23 + -69x + 18x2 = 23 + -23 + -3x + 3x

Combine like terms: 23 + -23 = 0
-23 + -69x + 18x2 = 0 + -3x + 3x
-23 + -69x + 18x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-23 + -69x + 18x2 = 0

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

Divide each side by '18'.
-1.277777778 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '1.277777778' to each side of the equation.
-1.277777778 + -3.833333333x + 1.277777778 + x2 = 0 + 1.277777778

Reorder the terms:
-1.277777778 + 1.277777778 + -3.833333333x + x2 = 0 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + -3.833333333x + x2 = 0 + 1.277777778
-3.833333333x + x2 = 0 + 1.277777778

Combine like terms: 0 + 1.277777778 = 1.277777778
-3.833333333x + x2 = 1.277777778

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = 1.277777778 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = 1.277777778 + 3.673611112

Combine like terms: 1.277777778 + 3.673611112 = 4.95138889
3.673611112 + -3.833333333x + x2 = 4.95138889

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = 4.95138889

Calculate the square root of the right side: 2.225171654

Break this problem into two subproblems by setting 
(x + -1.916666667) equal to 2.225171654 and -2.225171654.

Subproblem 1
x + -1.916666667 = 2.225171654

Simplifying
x + -1.916666667 = 2.225171654

Reorder the terms:
-1.916666667 + x = 2.225171654

Solving
-1.916666667 + x = 2.225171654

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = 2.225171654 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = 2.225171654 + 1.916666667
x = 2.225171654 + 1.916666667

Combine like terms: 2.225171654 + 1.916666667 = 4.141838321
x = 4.141838321

Simplifying
x = 4.141838321

Subproblem 2
x + -1.916666667 = -2.225171654

Simplifying
x + -1.916666667 = -2.225171654

Reorder the terms:
-1.916666667 + x = -2.225171654

Solving
-1.916666667 + x = -2.225171654

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = -2.225171654 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = -2.225171654 + 1.916666667
x = -2.225171654 + 1.916666667

Combine like terms: -2.225171654 + 1.916666667 = -0.308504987
x = -0.308504987

Simplifying
x = -0.308504987

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.141838321, -0.308504987}