9515=x^2-15x+65

Solution for 9515=x^2-15x+65 equation:

Simplifying
9515 = x2 + -15x + 65

Reorder the terms:
9515 = 65 + -15x + x2

Solving
9515 = 65 + -15x + x2

Solving for variable 'x'.

Combine like terms: 9515 + -65 = 9450
9450 + 15x + -1x2 = 65 + -15x + x2 + -65 + 15x + -1x2

Reorder the terms:
9450 + 15x + -1x2 = 65 + -65 + -15x + 15x + x2 + -1x2

Combine like terms: 65 + -65 = 0
9450 + 15x + -1x2 = 0 + -15x + 15x + x2 + -1x2
9450 + 15x + -1x2 = -15x + 15x + x2 + -1x2

Combine like terms: -15x + 15x = 0
9450 + 15x + -1x2 = 0 + x2 + -1x2
9450 + 15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9450 + 15x + -1x2 = 0

Factor a trinomial.
(105 + -1x)(90 + x) = 0

Subproblem 1
Set the factor '(105 + -1x)' equal to zero and attempt to solve:

Simplifying
105 + -1x = 0

Solving
105 + -1x = 0

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

Add '-105' to each side of the equation.
105 + -105 + -1x = 0 + -105

Combine like terms: 105 + -105 = 0
0 + -1x = 0 + -105
-1x = 0 + -105

Combine like terms: 0 + -105 = -105
-1x = -105

Divide each side by '-1'.
x = 105

Simplifying
x = 105
Subproblem 2
Set the factor '(90 + x)' equal to zero and attempt to solve:

Simplifying
90 + x = 0

Solving
90 + x = 0

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

Add '-90' to each side of the equation.
90 + -90 + x = 0 + -90

Combine like terms: 90 + -90 = 0
0 + x = 0 + -90
x = 0 + -90

Combine like terms: 0 + -90 = -90
x = -90

Simplifying
x = -90
Solution
x = {105, -90}