15-1=10+4(x+11)2x+20

Solution for 15-1=10+4(x+11)2x+20 equation:

Simplifying
15 + -1 = 10 + 4(x + 11) * 2x + 20

Combine like terms: 15 + -1 = 14
14 = 10 + 4(x + 11) * 2x + 20

Reorder the terms:
14 = 10 + 4(11 + x) * 2x + 20

Reorder the terms for easier multiplication:
14 = 10 + 4 * 2x(11 + x) + 20

Multiply 4 * 2
14 = 10 + 8x(11 + x) + 20
14 = 10 + (11 * 8x + x * 8x) + 20
14 = 10 + (88x + 8x2) + 20

Reorder the terms:
14 = 10 + 20 + 88x + 8x2

Combine like terms: 10 + 20 = 30
14 = 30 + 88x + 8x2

Solving
14 = 30 + 88x + 8x2

Solving for variable 'x'.

Combine like terms: 14 + -30 = -16
-16 + -88x + -8x2 = 30 + 88x + 8x2 + -30 + -88x + -8x2

Reorder the terms:
-16 + -88x + -8x2 = 30 + -30 + 88x + -88x + 8x2 + -8x2

Combine like terms: 30 + -30 = 0
-16 + -88x + -8x2 = 0 + 88x + -88x + 8x2 + -8x2
-16 + -88x + -8x2 = 88x + -88x + 8x2 + -8x2

Combine like terms: 88x + -88x = 0
-16 + -88x + -8x2 = 0 + 8x2 + -8x2
-16 + -88x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-16 + -88x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-8'.
-8(2 + 11x + x2) = 0

Ignore the factor -8.
Subproblem 1
Set the factor '(2 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 11x + x2 = 0

Solving
2 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 11x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 11x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 11x + x2 = 0 + -2
11x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
11x + x2 = -2

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -2 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -2 + 30.25

Combine like terms: -2 + 30.25 = 28.25
30.25 + 11x + x2 = 28.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
x + 5.5 = 5.315072906

Simplifying
x + 5.5 = 5.315072906

Reorder the terms:
5.5 + x = 5.315072906

Solving
5.5 + x = 5.315072906

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 5.315072906 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.315072906 + -5.5
x = 5.315072906 + -5.5

Combine like terms: 5.315072906 + -5.5 = -0.184927094
x = -0.184927094

Simplifying
x = -0.184927094

Subproblem 2
x + 5.5 = -5.315072906

Simplifying
x + 5.5 = -5.315072906

Reorder the terms:
5.5 + x = -5.315072906

Solving
5.5 + x = -5.315072906

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -5.315072906 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.315072906 + -5.5
x = -5.315072906 + -5.5

Combine like terms: -5.315072906 + -5.5 = -10.815072906
x = -10.815072906

Simplifying
x = -10.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.184927094, -10.815072906}
Solution
x = {-0.184927094, -10.815072906}