x^2-15x=9+x-64

Solution for x^2-15x=9+x-64 equation:

Simplifying
x2 + -15x = 9 + x + -64

Reorder the terms:
-15x + x2 = 9 + x + -64

Reorder the terms:
-15x + x2 = 9 + -64 + x

Combine like terms: 9 + -64 = -55
-15x + x2 = -55 + x

Solving
-15x + x2 = -55 + x

Solving for variable 'x'.

Reorder the terms:
55 + -15x + -1x + x2 = -55 + x + 55 + -1x

Combine like terms: -15x + -1x = -16x
55 + -16x + x2 = -55 + x + 55 + -1x

Reorder the terms:
55 + -16x + x2 = -55 + 55 + x + -1x

Combine like terms: -55 + 55 = 0
55 + -16x + x2 = 0 + x + -1x
55 + -16x + x2 = x + -1x

Combine like terms: x + -1x = 0
55 + -16x + x2 = 0

Factor a trinomial.
(5 + -1x)(11 + -1x) = 0

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {5, 11}