-6x-(x^2-9x+x-9)=-15

Solution for -6x-(x^2-9x+x-9)=-15 equation:

Simplifying
-6x + -1(x2 + -9x + x + -9) = -15

Reorder the terms:
-6x + -1(-9 + -9x + x + x2) = -15

Combine like terms: -9x + x = -8x
-6x + -1(-9 + -8x + x2) = -15
-6x + (-9 * -1 + -8x * -1 + x2 * -1) = -15
-6x + (9 + 8x + -1x2) = -15

Reorder the terms:
9 + -6x + 8x + -1x2 = -15

Combine like terms: -6x + 8x = 2x
9 + 2x + -1x2 = -15

Solving
9 + 2x + -1x2 = -15

Solving for variable 'x'.

Reorder the terms:
9 + 15 + 2x + -1x2 = -15 + 15

Combine like terms: 9 + 15 = 24
24 + 2x + -1x2 = -15 + 15

Combine like terms: -15 + 15 = 0
24 + 2x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {6, -4}