2a^3=12a^2

Solution for 2a^3=12a^2 equation:

Simplifying
2a3 = 12a2

Solving
2a3 = 12a2

Solving for variable 'a'.

Reorder the terms:
-12a2 + 2a3 = 12a2 + -12a2

Combine like terms: 12a2 + -12a2 = 0
-12a2 + 2a3 = 0

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(-6 + a) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
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
Solution
a = {0, 6}