6a^3-2a=a^2

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

Simplifying
6a3 + -2a = a2

Reorder the terms:
-2a + 6a3 = a2

Solving
-2a + 6a3 = a2

Solving for variable 'a'.

Reorder the terms:
-2a + -1a2 + 6a3 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-2a + -1a2 + 6a3 = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 3
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

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

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

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {0, -0.5, 0.6666666667}