(x+2)(x-5)=6x+x^2+x^2-5

Solution for (x+2)(x-5)=6x+x^2+x^2-5 equation:

Simplifying
(x + 2)(x + -5) = 6x + x2 + x2 + -5

Reorder the terms:
(2 + x)(x + -5) = 6x + x2 + x2 + -5

Reorder the terms:
(2 + x)(-5 + x) = 6x + x2 + x2 + -5

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = 6x + x2 + x2 + -5
((-5 * 2 + x * 2) + x(-5 + x)) = 6x + x2 + x2 + -5
((-10 + 2x) + x(-5 + x)) = 6x + x2 + x2 + -5
(-10 + 2x + (-5 * x + x * x)) = 6x + x2 + x2 + -5
(-10 + 2x + (-5x + x2)) = 6x + x2 + x2 + -5

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = 6x + x2 + x2 + -5

Reorder the terms:
-10 + -3x + x2 = -5 + 6x + x2 + x2

Combine like terms: x2 + x2 = 2x2
-10 + -3x + x2 = -5 + 6x + 2x2

Solving
-10 + -3x + x2 = -5 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 5 + -3x + -6x + x2 + -2x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Combine like terms: -10 + 5 = -5
-5 + -3x + -6x + x2 + -2x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Combine like terms: -3x + -6x = -9x
-5 + -9x + x2 + -2x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-5 + -9x + -1x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Reorder the terms:
-5 + -9x + -1x2 = -5 + 5 + 6x + -6x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
-5 + -9x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
-5 + -9x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-5 + -9x + -1x2 = 0 + 2x2 + -2x2
-5 + -9x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 9x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 9x + x2 = 0

Solving
5 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 9x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 9x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9x + x2 = 0 + -5
9x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
9x + x2 = -5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + 9x + x2 = 15.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + 4.5 = 3.905124838

Simplifying
x + 4.5 = 3.905124838

Reorder the terms:
4.5 + x = 3.905124838

Solving
4.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.905124838 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.905124838 + -4.5
x = 3.905124838 + -4.5

Combine like terms: 3.905124838 + -4.5 = -0.594875162
x = -0.594875162

Simplifying
x = -0.594875162

Subproblem 2
x + 4.5 = -3.905124838

Simplifying
x + 4.5 = -3.905124838

Reorder the terms:
4.5 + x = -3.905124838

Solving
4.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.905124838 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.905124838 + -4.5
x = -3.905124838 + -4.5

Combine like terms: -3.905124838 + -4.5 = -8.405124838
x = -8.405124838

Simplifying
x = -8.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.594875162, -8.405124838}
Solution
x = {-0.594875162, -8.405124838}