3y^2-33y=-30

Solution for 3y^2-33y=-30 equation:

Simplifying
3y2 + -33y = -30

Reorder the terms:
-33y + 3y2 = -30

Solving
-33y + 3y2 = -30

Solving for variable 'y'.

Reorder the terms:
30 + -33y + 3y2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -33y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -11y + y2) = 0

Factor a trinomial.
3((1 + -1y)(10 + -1y)) = 0

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {1, 10}