30y^2+9y-3=0

Solution for 30y^2+9y-3=0 equation:

Simplifying
30y2 + 9y + -3 = 0

Reorder the terms:
-3 + 9y + 30y2 = 0

Solving
-3 + 9y + 30y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 3y + 10y2) = 0

Factor a trinomial.
3((-1 + -2y)(1 + -5y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

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

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

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

Simplifying
y = -0.5
Subproblem 2
Set the factor '(1 + -5y)' equal to zero and attempt to solve:

Simplifying
1 + -5y = 0

Solving
1 + -5y = 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 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {-0.5, 0.2}