a^3-8a^2-48a=0

Solution for a^3-8a^2-48a=0 equation:

Simplifying
a3 + -8a2 + -48a = 0

Reorder the terms:
-48a + -8a2 + a3 = 0

Solving
-48a + -8a2 + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-48 + -8a + a2) = 0

Factor a trinomial.
a((-4 + -1a)(12 + -1a)) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
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 3
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {0, -4, 12}