x(x+5)=2(x+15)(x-2)+112

Solution for x(x+5)=2(x+15)(x-2)+112 equation:

Simplifying
x(x + 5) = 2(x + 15)(x + -2) + 112

Reorder the terms:
x(5 + x) = 2(x + 15)(x + -2) + 112
(5 * x + x * x) = 2(x + 15)(x + -2) + 112
(5x + x2) = 2(x + 15)(x + -2) + 112

Reorder the terms:
5x + x2 = 2(15 + x)(x + -2) + 112

Reorder the terms:
5x + x2 = 2(15 + x)(-2 + x) + 112

Multiply (15 + x) * (-2 + x)
5x + x2 = 2(15(-2 + x) + x(-2 + x)) + 112
5x + x2 = 2((-2 * 15 + x * 15) + x(-2 + x)) + 112
5x + x2 = 2((-30 + 15x) + x(-2 + x)) + 112
5x + x2 = 2(-30 + 15x + (-2 * x + x * x)) + 112
5x + x2 = 2(-30 + 15x + (-2x + x2)) + 112

Combine like terms: 15x + -2x = 13x
5x + x2 = 2(-30 + 13x + x2) + 112
5x + x2 = (-30 * 2 + 13x * 2 + x2 * 2) + 112
5x + x2 = (-60 + 26x + 2x2) + 112

Reorder the terms:
5x + x2 = -60 + 112 + 26x + 2x2

Combine like terms: -60 + 112 = 52
5x + x2 = 52 + 26x + 2x2

Solving
5x + x2 = 52 + 26x + 2x2

Solving for variable 'x'.

Reorder the terms:
-52 + 5x + -26x + x2 + -2x2 = 52 + 26x + 2x2 + -52 + -26x + -2x2

Combine like terms: 5x + -26x = -21x
-52 + -21x + x2 + -2x2 = 52 + 26x + 2x2 + -52 + -26x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-52 + -21x + -1x2 = 52 + 26x + 2x2 + -52 + -26x + -2x2

Reorder the terms:
-52 + -21x + -1x2 = 52 + -52 + 26x + -26x + 2x2 + -2x2

Combine like terms: 52 + -52 = 0
-52 + -21x + -1x2 = 0 + 26x + -26x + 2x2 + -2x2
-52 + -21x + -1x2 = 26x + -26x + 2x2 + -2x2

Combine like terms: 26x + -26x = 0
-52 + -21x + -1x2 = 0 + 2x2 + -2x2
-52 + -21x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-52 + -21x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(52 + 21x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(52 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
52 + 21x + x2 = 0

Solving
52 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + 21x + -52 + x2 = 0 + -52

Reorder the terms:
52 + -52 + 21x + x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 21x + x2 = 0 + -52
21x + x2 = 0 + -52

Combine like terms: 0 + -52 = -52
21x + x2 = -52

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -52 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -52 + 110.25

Combine like terms: -52 + 110.25 = 58.25
110.25 + 21x + x2 = 58.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(x + 10.5) equal to 7.632168761 and -7.632168761.

Subproblem 1
x + 10.5 = 7.632168761

Simplifying
x + 10.5 = 7.632168761

Reorder the terms:
10.5 + x = 7.632168761

Solving
10.5 + x = 7.632168761

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 7.632168761 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 7.632168761 + -10.5
x = 7.632168761 + -10.5

Combine like terms: 7.632168761 + -10.5 = -2.867831239
x = -2.867831239

Simplifying
x = -2.867831239

Subproblem 2
x + 10.5 = -7.632168761

Simplifying
x + 10.5 = -7.632168761

Reorder the terms:
10.5 + x = -7.632168761

Solving
10.5 + x = -7.632168761

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -7.632168761 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -7.632168761 + -10.5
x = -7.632168761 + -10.5

Combine like terms: -7.632168761 + -10.5 = -18.132168761
x = -18.132168761

Simplifying
x = -18.132168761

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.867831239, -18.132168761}
Solution
x = {-2.867831239, -18.132168761}