x^2-15x+65=11565

Solution for x^2-15x+65=11565 equation:

Simplifying
x2 + -15x + 65 = 11565

Reorder the terms:
65 + -15x + x2 = 11565

Solving
65 + -15x + x2 = 11565

Solving for variable 'x'.

Reorder the terms:
65 + -11565 + -15x + x2 = 11565 + -11565

Combine like terms: 65 + -11565 = -11500
-11500 + -15x + x2 = 11565 + -11565

Combine like terms: 11565 + -11565 = 0
-11500 + -15x + x2 = 0

Factor a trinomial.
(-100 + -1x)(115 + -1x) = 0

Subproblem 1
Set the factor '(-100 + -1x)' equal to zero and attempt to solve:

Simplifying
-100 + -1x = 0

Solving
-100 + -1x = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1x = 0 + 100
-1x = 0 + 100

Combine like terms: 0 + 100 = 100
-1x = 100

Divide each side by '-1'.
x = -100

Simplifying
x = -100
Subproblem 2
Set the factor '(115 + -1x)' equal to zero and attempt to solve:

Simplifying
115 + -1x = 0

Solving
115 + -1x = 0

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

Add '-115' to each side of the equation.
115 + -115 + -1x = 0 + -115

Combine like terms: 115 + -115 = 0
0 + -1x = 0 + -115
-1x = 0 + -115

Combine like terms: 0 + -115 = -115
-1x = -115

Divide each side by '-1'.
x = 115

Simplifying
x = 115
Solution
x = {-100, 115}