12a^3=16a^2+3a

Solution for 12a^3=16a^2+3a equation:

Simplifying
12a3 = 16a2 + 3a

Reorder the terms:
12a3 = 3a + 16a2

Solving
12a3 = 3a + 16a2

Solving for variable 'a'.

Reorder the terms:
-3a + -16a2 + 12a3 = 3a + 16a2 + -3a + -16a2

Reorder the terms:
-3a + -16a2 + 12a3 = 3a + -3a + 16a2 + -16a2

Combine like terms: 3a + -3a = 0
-3a + -16a2 + 12a3 = 0 + 16a2 + -16a2
-3a + -16a2 + 12a3 = 16a2 + -16a2

Combine like terms: 16a2 + -16a2 = 0
-3a + -16a2 + 12a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-3 + -16a + 12a2) = 0

Factor a trinomial.
a((-1 + -6a)(3 + -2a)) = 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 '(-1 + -6a)' equal to zero and attempt to solve:

Simplifying
-1 + -6a = 0

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

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

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

Divide each side by '-6'.
a = -0.1666666667

Simplifying
a = -0.1666666667
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, -0.1666666667, 1.5}