-2a^2+26a-80=0

Solution for -2a^2+26a-80=0 equation:

Simplifying
-2a2 + 26a + -80 = 0

Reorder the terms:
-80 + 26a + -2a2 = 0

Solving
-80 + 26a + -2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 13a + -1a2) = 0

Factor a trinomial.
2((-8 + a)(5 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + a)' equal to zero and attempt to solve:

Simplifying
-8 + a = 0

Solving
-8 + a = 0

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

Add '8' to each side of the equation.
-8 + 8 + a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + a = 0 + 8
a = 0 + 8

Combine like terms: 0 + 8 = 8
a = 8

Simplifying
a = 8
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

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

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

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

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

Simplifying
a = 5
Solution
a = {8, 5}