15x+(-6x+5)-2-(-x+13)=-(7x+23)-x(3-2x)

Solution for 15x+(-6x+5)-2-(-x+13)=-(7x+23)-x(3-2x) equation:

Simplifying
15x + (-6x + 5) + -2 + -1(-1x + 13) = -1(7x + 23) + -1x(3 + -2x)

Reorder the terms:
15x + (5 + -6x) + -2 + -1(-1x + 13) = -1(7x + 23) + -1x(3 + -2x)

Remove parenthesis around (5 + -6x)
15x + 5 + -6x + -2 + -1(-1x + 13) = -1(7x + 23) + -1x(3 + -2x)

Reorder the terms:
15x + 5 + -6x + -2 + -1(13 + -1x) = -1(7x + 23) + -1x(3 + -2x)
15x + 5 + -6x + -2 + (13 * -1 + -1x * -1) = -1(7x + 23) + -1x(3 + -2x)
15x + 5 + -6x + -2 + (-13 + 1x) = -1(7x + 23) + -1x(3 + -2x)

Reorder the terms:
5 + -2 + -13 + 15x + -6x + 1x = -1(7x + 23) + -1x(3 + -2x)

Combine like terms: 5 + -2 = 3
3 + -13 + 15x + -6x + 1x = -1(7x + 23) + -1x(3 + -2x)

Combine like terms: 3 + -13 = -10
-10 + 15x + -6x + 1x = -1(7x + 23) + -1x(3 + -2x)

Combine like terms: 15x + -6x = 9x
-10 + 9x + 1x = -1(7x + 23) + -1x(3 + -2x)

Combine like terms: 9x + 1x = 10x
-10 + 10x = -1(7x + 23) + -1x(3 + -2x)

Reorder the terms:
-10 + 10x = -1(23 + 7x) + -1x(3 + -2x)
-10 + 10x = (23 * -1 + 7x * -1) + -1x(3 + -2x)
-10 + 10x = (-23 + -7x) + -1x(3 + -2x)
-10 + 10x = -23 + -7x + (3 * -1x + -2x * -1x)
-10 + 10x = -23 + -7x + (-3x + 2x2)

Combine like terms: -7x + -3x = -10x
-10 + 10x = -23 + -10x + 2x2

Solving
-10 + 10x = -23 + -10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 23 + 10x + 10x + -2x2 = -23 + -10x + 2x2 + 23 + 10x + -2x2

Combine like terms: -10 + 23 = 13
13 + 10x + 10x + -2x2 = -23 + -10x + 2x2 + 23 + 10x + -2x2

Combine like terms: 10x + 10x = 20x
13 + 20x + -2x2 = -23 + -10x + 2x2 + 23 + 10x + -2x2

Reorder the terms:
13 + 20x + -2x2 = -23 + 23 + -10x + 10x + 2x2 + -2x2

Combine like terms: -23 + 23 = 0
13 + 20x + -2x2 = 0 + -10x + 10x + 2x2 + -2x2
13 + 20x + -2x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
13 + 20x + -2x2 = 0 + 2x2 + -2x2
13 + 20x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
13 + 20x + -2x2 = 0

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

Divide each side by '-2'.
-6.5 + -10x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -10x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -10x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -10x + x2 = 0 + 6.5
-10x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-10x + x2 = 6.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 6.5 + 25

Reorder the terms:
25 + -10x + x2 = 6.5 + 25

Combine like terms: 6.5 + 25 = 31.5
25 + -10x + x2 = 31.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 31.5

Calculate the square root of the right side: 5.61248608

Break this problem into two subproblems by setting 
(x + -5) equal to 5.61248608 and -5.61248608.

Subproblem 1
x + -5 = 5.61248608

Simplifying
x + -5 = 5.61248608

Reorder the terms:
-5 + x = 5.61248608

Solving
-5 + x = 5.61248608

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.61248608 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.61248608 + 5
x = 5.61248608 + 5

Combine like terms: 5.61248608 + 5 = 10.61248608
x = 10.61248608

Simplifying
x = 10.61248608

Subproblem 2
x + -5 = -5.61248608

Simplifying
x + -5 = -5.61248608

Reorder the terms:
-5 + x = -5.61248608

Solving
-5 + x = -5.61248608

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.61248608 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.61248608 + 5
x = -5.61248608 + 5

Combine like terms: -5.61248608 + 5 = -0.61248608
x = -0.61248608

Simplifying
x = -0.61248608

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.61248608, -0.61248608}