-a^2+26a-165=0

Solution for -a^2+26a-165=0 equation:

Simplifying
-1a2 + 26a + -165 = 0

Reorder the terms:
-165 + 26a + -1a2 = 0

Solving
-165 + 26a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-15 + a)(11 + -1a) = 0

Subproblem 1
Set the factor '(-15 + a)' equal to zero and attempt to solve:

Simplifying
-15 + a = 0

Solving
-15 + a = 0

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

Add '15' to each side of the equation.
-15 + 15 + a = 0 + 15

Combine like terms: -15 + 15 = 0
0 + a = 0 + 15
a = 0 + 15

Combine like terms: 0 + 15 = 15
a = 15

Simplifying
a = 15
Subproblem 2
Set the factor '(11 + -1a)' equal to zero and attempt to solve:

Simplifying
11 + -1a = 0

Solving
11 + -1a = 0

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

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

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

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

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

Simplifying
a = 11
Solution
a = {15, 11}