=6a^2-48a-120

Solution for =6a^2-48a-120 equation:

Simplifying
0 = 6a2 + -48a + -120

Reorder the terms:
0 = -120 + -48a + 6a2

Solving
0 = -120 + -48a + 6a2

Solving for variable 'a'.

Combine like terms: 0 + 120 = 120
120 + 48a + -6a2 = -120 + -48a + 6a2 + 120 + 48a + -6a2

Reorder the terms:
120 + 48a + -6a2 = -120 + 120 + -48a + 48a + 6a2 + -6a2

Combine like terms: -120 + 120 = 0
120 + 48a + -6a2 = 0 + -48a + 48a + 6a2 + -6a2
120 + 48a + -6a2 = -48a + 48a + 6a2 + -6a2

Combine like terms: -48a + 48a = 0
120 + 48a + -6a2 = 0 + 6a2 + -6a2
120 + 48a + -6a2 = 6a2 + -6a2

Combine like terms: 6a2 + -6a2 = 0
120 + 48a + -6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + 8a + -1a2) = 0

Factor a trinomial.
6((10 + -1a)(2 + a)) = 0

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

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
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 = {10, -2}