25a^2-10a-80=0

Solution for 25a^2-10a-80=0 equation:

Simplifying
25a2 + -10a + -80 = 0

Reorder the terms:
-80 + -10a + 25a2 = 0

Solving
-80 + -10a + 25a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -2a + 5a2) = 0

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

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

Simplifying
-8 + -5a = 0

Solving
-8 + -5a = 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 + -5a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5a = 0 + 8
-5a = 0 + 8

Combine like terms: 0 + 8 = 8
-5a = 8

Divide each side by '-5'.
a = -1.6

Simplifying
a = -1.6
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.6, 2}