10a^2+20a-80=0

Solution for 10a^2+20a-80=0 equation:

Simplifying
10a2 + 20a + -80 = 0

Reorder the terms:
-80 + 20a + 10a2 = 0

Solving
-80 + 20a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 2a + a2) = 0

Factor a trinomial.
10((-4 + -1a)(2 + -1a)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
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 = {-4, 2}