x(3x+x)=8(8+x+2)

Solution for x(3x+x)=8(8+x+2) equation:

Simplifying
x(3x + x) = 8(8 + x + 2)

Combine like terms: 3x + x = 4x
x(4x) = 8(8 + x + 2)

Remove parenthesis around (4x)
x * 4x = 8(8 + x + 2)

Reorder the terms for easier multiplication:
4x * x = 8(8 + x + 2)

Multiply x * x
4x2 = 8(8 + x + 2)

Reorder the terms:
4x2 = 8(8 + 2 + x)

Combine like terms: 8 + 2 = 10
4x2 = 8(10 + x)
4x2 = (10 * 8 + x * 8)
4x2 = (80 + 8x)

Solving
4x2 = 80 + 8x

Solving for variable 'x'.

Reorder the terms:
-80 + -8x + 4x2 = 80 + 8x + -80 + -8x

Reorder the terms:
-80 + -8x + 4x2 = 80 + -80 + 8x + -8x

Combine like terms: 80 + -80 = 0
-80 + -8x + 4x2 = 0 + 8x + -8x
-80 + -8x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-80 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + -2x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-20 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -2x + x2 = 0

Solving
-20 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -2x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2x + x2 = 0 + 20
-2x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2x + x2 = 20

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 20 + 1

Reorder the terms:
1 + -2x + x2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2x + x2 = 21

Factor a perfect square on the left side:
(x + -1)(x + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
x + -1 = 4.582575695

Simplifying
x + -1 = 4.582575695

Reorder the terms:
-1 + x = 4.582575695

Solving
-1 + x = 4.582575695

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.582575695 + 1
x = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
x = 5.582575695

Simplifying
x = 5.582575695

Subproblem 2
x + -1 = -4.582575695

Simplifying
x + -1 = -4.582575695

Reorder the terms:
-1 + x = -4.582575695

Solving
-1 + x = -4.582575695

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.582575695 + 1
x = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
x = -3.582575695

Simplifying
x = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.582575695, -3.582575695}
Solution
x = {5.582575695, -3.582575695}