2a^2+6a=80

Solution for 2a^2+6a=80 equation:

Simplifying
2a2 + 6a = 80

Reorder the terms:
6a + 2a2 = 80

Solving
6a + 2a2 = 80

Solving for variable 'a'.

Reorder the terms:
-80 + 6a + 2a2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 6a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 3a + a2) = 0

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

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

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 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 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
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}