x^2+(x-5)(x+3)=126

Solution for x^2+(x-5)(x+3)=126 equation:

Simplifying
x2 + (x + -5)(x + 3) = 126

Reorder the terms:
x2 + (-5 + x)(x + 3) = 126

Reorder the terms:
x2 + (-5 + x)(3 + x) = 126

Multiply (-5 + x) * (3 + x)
x2 + (-5(3 + x) + x(3 + x)) = 126
x2 + ((3 * -5 + x * -5) + x(3 + x)) = 126
x2 + ((-15 + -5x) + x(3 + x)) = 126
x2 + (-15 + -5x + (3 * x + x * x)) = 126
x2 + (-15 + -5x + (3x + x2)) = 126

Combine like terms: -5x + 3x = -2x
x2 + (-15 + -2x + x2) = 126

Reorder the terms:
-15 + -2x + x2 + x2 = 126

Combine like terms: x2 + x2 = 2x2
-15 + -2x + 2x2 = 126

Solving
-15 + -2x + 2x2 = 126

Solving for variable 'x'.

Reorder the terms:
-15 + -126 + -2x + 2x2 = 126 + -126

Combine like terms: -15 + -126 = -141
-141 + -2x + 2x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-141 + -2x + 2x2 = 0

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

Divide each side by '2'.
-70.5 + -1x + x2 = 0

Move the constant term to the right:

Add '70.5' to each side of the equation.
-70.5 + -1x + 70.5 + x2 = 0 + 70.5

Reorder the terms:
-70.5 + 70.5 + -1x + x2 = 0 + 70.5

Combine like terms: -70.5 + 70.5 = 0.0
0.0 + -1x + x2 = 0 + 70.5
-1x + x2 = 0 + 70.5

Combine like terms: 0 + 70.5 = 70.5
-1x + x2 = 70.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 70.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 70.5 + 0.25

Combine like terms: 70.5 + 0.25 = 70.75
0.25 + -1x + x2 = 70.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 70.75

Calculate the square root of the right side: 8.411301921

Break this problem into two subproblems by setting 
(x + -0.5) equal to 8.411301921 and -8.411301921.

Subproblem 1
x + -0.5 = 8.411301921

Simplifying
x + -0.5 = 8.411301921

Reorder the terms:
-0.5 + x = 8.411301921

Solving
-0.5 + x = 8.411301921

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 8.411301921 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 8.411301921 + 0.5
x = 8.411301921 + 0.5

Combine like terms: 8.411301921 + 0.5 = 8.911301921
x = 8.911301921

Simplifying
x = 8.911301921

Subproblem 2
x + -0.5 = -8.411301921

Simplifying
x + -0.5 = -8.411301921

Reorder the terms:
-0.5 + x = -8.411301921

Solving
-0.5 + x = -8.411301921

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -8.411301921 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -8.411301921 + 0.5
x = -8.411301921 + 0.5

Combine like terms: -8.411301921 + 0.5 = -7.911301921
x = -7.911301921

Simplifying
x = -7.911301921

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.911301921, -7.911301921}