6y^2-3y=30

Solution for 6y^2-3y=30 equation:

Simplifying
6y2 + -3y = 30

Reorder the terms:
-3y + 6y2 = 30

Solving
-3y + 6y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + -3y + 6y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -3y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1y + 2y2) = 0

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

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

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

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-2, 2.5}