10a^2+80a+120=0

Solution for 10a^2+80a+120=0 equation:

Simplifying
10a2 + 80a + 120 = 0

Reorder the terms:
120 + 80a + 10a2 = 0

Solving
120 + 80a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(12 + 8a + a2) = 0

Factor a trinomial.
10((6 + a)(2 + a)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

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

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

Simplifying
a = -2
Solution
a = {-6, -2}