a^3+2a^2=48a

Solution for a^3+2a^2=48a equation:

Simplifying
a3 + 2a2 = 48a

Reorder the terms:
2a2 + a3 = 48a

Solving
2a2 + a3 = 48a

Solving for variable 'a'.

Reorder the terms:
-48a + 2a2 + a3 = 48a + -48a

Combine like terms: 48a + -48a = 0
-48a + 2a2 + a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-48 + 2a + a2) = 0

Factor a trinomial.
a((-8 + -1a)(6 + -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 '(-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 3
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0, -8, 6}