8+2(x-3)=4(x-5)3(20-x)

Solution for 8+2(x-3)=4(x-5)3(20-x) equation:

Simplifying
8 + 2(x + -3) = 4(x + -5) * 3(20 + -1x)

Reorder the terms:
8 + 2(-3 + x) = 4(x + -5) * 3(20 + -1x)
8 + (-3 * 2 + x * 2) = 4(x + -5) * 3(20 + -1x)
8 + (-6 + 2x) = 4(x + -5) * 3(20 + -1x)

Combine like terms: 8 + -6 = 2
2 + 2x = 4(x + -5) * 3(20 + -1x)

Reorder the terms:
2 + 2x = 4(-5 + x) * 3(20 + -1x)

Reorder the terms for easier multiplication:
2 + 2x = 4 * 3(-5 + x)(20 + -1x)

Multiply 4 * 3
2 + 2x = 12(-5 + x)(20 + -1x)

Multiply (-5 + x) * (20 + -1x)
2 + 2x = 12(-5(20 + -1x) + x(20 + -1x))
2 + 2x = 12((20 * -5 + -1x * -5) + x(20 + -1x))
2 + 2x = 12((-100 + 5x) + x(20 + -1x))
2 + 2x = 12(-100 + 5x + (20 * x + -1x * x))
2 + 2x = 12(-100 + 5x + (20x + -1x2))

Combine like terms: 5x + 20x = 25x
2 + 2x = 12(-100 + 25x + -1x2)
2 + 2x = (-100 * 12 + 25x * 12 + -1x2 * 12)
2 + 2x = (-1200 + 300x + -12x2)

Solving
2 + 2x = -1200 + 300x + -12x2

Solving for variable 'x'.

Reorder the terms:
2 + 1200 + 2x + -300x + 12x2 = -1200 + 300x + -12x2 + 1200 + -300x + 12x2

Combine like terms: 2 + 1200 = 1202
1202 + 2x + -300x + 12x2 = -1200 + 300x + -12x2 + 1200 + -300x + 12x2

Combine like terms: 2x + -300x = -298x
1202 + -298x + 12x2 = -1200 + 300x + -12x2 + 1200 + -300x + 12x2

Reorder the terms:
1202 + -298x + 12x2 = -1200 + 1200 + 300x + -300x + -12x2 + 12x2

Combine like terms: -1200 + 1200 = 0
1202 + -298x + 12x2 = 0 + 300x + -300x + -12x2 + 12x2
1202 + -298x + 12x2 = 300x + -300x + -12x2 + 12x2

Combine like terms: 300x + -300x = 0
1202 + -298x + 12x2 = 0 + -12x2 + 12x2
1202 + -298x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
1202 + -298x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(601 + -149x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(601 + -149x + 6x2)' equal to zero and attempt to solve:

Simplifying
601 + -149x + 6x2 = 0

Solving
601 + -149x + 6x2 = 0

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

Divide each side by '6'.
100.1666667 + -24.83333333x + x2 = 0

Move the constant term to the right:

Add '-100.1666667' to each side of the equation.
100.1666667 + -24.83333333x + -100.1666667 + x2 = 0 + -100.1666667

Reorder the terms:
100.1666667 + -100.1666667 + -24.83333333x + x2 = 0 + -100.1666667

Combine like terms: 100.1666667 + -100.1666667 = 0.0000000
0.0000000 + -24.83333333x + x2 = 0 + -100.1666667
-24.83333333x + x2 = 0 + -100.1666667

Combine like terms: 0 + -100.1666667 = -100.1666667
-24.83333333x + x2 = -100.1666667

The x term is -24.83333333x.  Take half its coefficient (-12.41666667).
Square it (154.1736112) and add it to both sides.

Add '154.1736112' to each side of the equation.
-24.83333333x + 154.1736112 + x2 = -100.1666667 + 154.1736112

Reorder the terms:
154.1736112 + -24.83333333x + x2 = -100.1666667 + 154.1736112

Combine like terms: -100.1666667 + 154.1736112 = 54.0069445
154.1736112 + -24.83333333x + x2 = 54.0069445

Factor a perfect square on the left side:
(x + -12.41666667)(x + -12.41666667) = 54.0069445

Calculate the square root of the right side: 7.348941727

Break this problem into two subproblems by setting 
(x + -12.41666667) equal to 7.348941727 and -7.348941727.

Subproblem 1
x + -12.41666667 = 7.348941727

Simplifying
x + -12.41666667 = 7.348941727

Reorder the terms:
-12.41666667 + x = 7.348941727

Solving
-12.41666667 + x = 7.348941727

Solving for variable 'x'.

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

Add '12.41666667' to each side of the equation.
-12.41666667 + 12.41666667 + x = 7.348941727 + 12.41666667

Combine like terms: -12.41666667 + 12.41666667 = 0.00000000
0.00000000 + x = 7.348941727 + 12.41666667
x = 7.348941727 + 12.41666667

Combine like terms: 7.348941727 + 12.41666667 = 19.765608397
x = 19.765608397

Simplifying
x = 19.765608397

Subproblem 2
x + -12.41666667 = -7.348941727

Simplifying
x + -12.41666667 = -7.348941727

Reorder the terms:
-12.41666667 + x = -7.348941727

Solving
-12.41666667 + x = -7.348941727

Solving for variable 'x'.

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

Add '12.41666667' to each side of the equation.
-12.41666667 + 12.41666667 + x = -7.348941727 + 12.41666667

Combine like terms: -12.41666667 + 12.41666667 = 0.00000000
0.00000000 + x = -7.348941727 + 12.41666667
x = -7.348941727 + 12.41666667

Combine like terms: -7.348941727 + 12.41666667 = 5.067724943
x = 5.067724943

Simplifying
x = 5.067724943

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.765608397, 5.067724943}
Solution
x = {19.765608397, 5.067724943}