a=3a^2-a

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

Simplifying
a = 3a2 + -1a

Reorder the terms:
a = -1a + 3a2

Solving
a = -1a + 3a2

Solving for variable 'a'.

Combine like terms: a + a = 2a
2a + -3a2 = -1a + 3a2 + a + -3a2

Reorder the terms:
2a + -3a2 = -1a + a + 3a2 + -3a2

Combine like terms: -1a + a = 0
2a + -3a2 = 0 + 3a2 + -3a2
2a + -3a2 = 3a2 + -3a2

Combine like terms: 3a2 + -3a2 = 0
2a + -3a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(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 '(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, 0.6666666667}