(x+5)(x+5)+x(x-3)=132

Solution for (x+5)(x+5)+x(x-3)=132 equation:

Simplifying
(x + 5)(x + 5) + x(x + -3) = 132

Reorder the terms:
(5 + x)(x + 5) + x(x + -3) = 132

Reorder the terms:
(5 + x)(5 + x) + x(x + -3) = 132

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) + x(x + -3) = 132
((5 * 5 + x * 5) + x(5 + x)) + x(x + -3) = 132
((25 + 5x) + x(5 + x)) + x(x + -3) = 132
(25 + 5x + (5 * x + x * x)) + x(x + -3) = 132
(25 + 5x + (5x + x2)) + x(x + -3) = 132

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) + x(x + -3) = 132

Reorder the terms:
25 + 10x + x2 + x(-3 + x) = 132
25 + 10x + x2 + (-3 * x + x * x) = 132
25 + 10x + x2 + (-3x + x2) = 132

Reorder the terms:
25 + 10x + -3x + x2 + x2 = 132

Combine like terms: 10x + -3x = 7x
25 + 7x + x2 + x2 = 132

Combine like terms: x2 + x2 = 2x2
25 + 7x + 2x2 = 132

Solving
25 + 7x + 2x2 = 132

Solving for variable 'x'.

Reorder the terms:
25 + -132 + 7x + 2x2 = 132 + -132

Combine like terms: 25 + -132 = -107
-107 + 7x + 2x2 = 132 + -132

Combine like terms: 132 + -132 = 0
-107 + 7x + 2x2 = 0

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

Divide each side by '2'.
-53.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '53.5' to each side of the equation.
-53.5 + 3.5x + 53.5 + x2 = 0 + 53.5

Reorder the terms:
-53.5 + 53.5 + 3.5x + x2 = 0 + 53.5

Combine like terms: -53.5 + 53.5 = 0.0
0.0 + 3.5x + x2 = 0 + 53.5
3.5x + x2 = 0 + 53.5

Combine like terms: 0 + 53.5 = 53.5
3.5x + x2 = 53.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 53.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 53.5 + 3.0625

Combine like terms: 53.5 + 3.0625 = 56.5625
3.0625 + 3.5x + x2 = 56.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 56.5625

Calculate the square root of the right side: 7.520804478

Break this problem into two subproblems by setting 
(x + 1.75) equal to 7.520804478 and -7.520804478.

Subproblem 1
x + 1.75 = 7.520804478

Simplifying
x + 1.75 = 7.520804478

Reorder the terms:
1.75 + x = 7.520804478

Solving
1.75 + x = 7.520804478

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 7.520804478 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 7.520804478 + -1.75
x = 7.520804478 + -1.75

Combine like terms: 7.520804478 + -1.75 = 5.770804478
x = 5.770804478

Simplifying
x = 5.770804478

Subproblem 2
x + 1.75 = -7.520804478

Simplifying
x + 1.75 = -7.520804478

Reorder the terms:
1.75 + x = -7.520804478

Solving
1.75 + x = -7.520804478

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -7.520804478 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -7.520804478 + -1.75
x = -7.520804478 + -1.75

Combine like terms: -7.520804478 + -1.75 = -9.270804478
x = -9.270804478

Simplifying
x = -9.270804478

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.770804478, -9.270804478}