3y^2=-y

Solution for 3y^2=-y equation:

Simplifying
3y2 = -1y

Solving
3y2 = -1y

Solving for variable 'y'.

Reorder the terms:
y + 3y2 = -1y + y

Combine like terms: -1y + y = 0
y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + 3y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {0, -0.3333333333}