5a^2bc+25abc-120bc=0

Solution for 5a^2bc+25abc-120bc=0 equation:

Simplifying
5a2bc + 25abc + -120bc = 0

Reorder the terms:
25abc + 5a2bc + -120bc = 0

Solving
25abc + 5a2bc + -120bc = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5bc'.
5bc(5a + a2 + -24) = 0

Factor a trinomial.
5bc((a + -3)(a + 8)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'bc' equal to zero and attempt to solve:

Simplifying
bc = 0

Solving
bc = 0

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

Add '-1bc' to each side of the equation.
bc + -1bc = 0 + -1bc
Remove the zero:
0 = -1bc

Simplifying
0 = -1bc

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(a + -3)' equal to zero and attempt to solve:

Simplifying
a + -3 = 0

Reorder the terms:
-3 + a = 0

Solving
-3 + a = 0

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

Add '3' to each side of the equation.
-3 + 3 + a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + a = 0 + 3
a = 0 + 3

Combine like terms: 0 + 3 = 3
a = 3

Simplifying
a = 3
Subproblem 3
Set the factor '(a + 8)' equal to zero and attempt to solve:

Simplifying
a + 8 = 0

Reorder the terms:
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
Solution
a = {3, -8}