12a^3-6a^2=18a

Solution for 12a^3-6a^2=18a equation:

Simplifying
12a3 + -6a2 = 18a

Reorder the terms:
-6a2 + 12a3 = 18a

Solving
-6a2 + 12a3 = 18a

Solving for variable 'a'.

Reorder the terms:
-18a + -6a2 + 12a3 = 18a + -18a

Combine like terms: 18a + -18a = 0
-18a + -6a2 + 12a3 = 0

Factor out the Greatest Common Factor (GCF), '6a'.
6a(-3 + -1a + 2a2) = 0

Factor a trinomial.
6a((-1 + -1a)(3 + -2a)) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {0, -1, 1.5}