8(8+x+12)=x(x+3x)

Solution for 8(8+x+12)=x(x+3x) equation:

Simplifying
8(8 + x + 12) = x(x + 3x)

Reorder the terms:
8(8 + 12 + x) = x(x + 3x)

Combine like terms: 8 + 12 = 20
8(20 + x) = x(x + 3x)
(20 * 8 + x * 8) = x(x + 3x)
(160 + 8x) = x(x + 3x)

Combine like terms: x + 3x = 4x
160 + 8x = x(4x)

Remove parenthesis around (4x)
160 + 8x = x * 4x

Reorder the terms for easier multiplication:
160 + 8x = 4x * x

Multiply x * x
160 + 8x = 4x2

Solving
160 + 8x = 4x2

Solving for variable 'x'.

Combine like terms: 4x2 + -4x2 = 0
160 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + 2x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(40 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
40 + 2x + -1x2 = 0

Solving
40 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + -2x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -2x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -2x + x2 = 0 + 40
-2x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2x + x2 = 40

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 = 40 + 1

Reorder the terms:
1 + -2x + x2 = 40 + 1

Combine like terms: 40 + 1 = 41
1 + -2x + x2 = 41

Factor a perfect square on the left side:
(x + -1)(x + -1) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -1) equal to 6.403124237 and -6.403124237.

Subproblem 1
x + -1 = 6.403124237

Simplifying
x + -1 = 6.403124237

Reorder the terms:
-1 + x = 6.403124237

Solving
-1 + x = 6.403124237

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 = 6.403124237 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.403124237 + 1
x = 6.403124237 + 1

Combine like terms: 6.403124237 + 1 = 7.403124237
x = 7.403124237

Simplifying
x = 7.403124237

Subproblem 2
x + -1 = -6.403124237

Simplifying
x + -1 = -6.403124237

Reorder the terms:
-1 + x = -6.403124237

Solving
-1 + x = -6.403124237

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 = -6.403124237 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.403124237 + 1
x = -6.403124237 + 1

Combine like terms: -6.403124237 + 1 = -5.403124237
x = -5.403124237

Simplifying
x = -5.403124237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.403124237, -5.403124237}
Solution
x = {7.403124237, -5.403124237}