2y^2+5y-33=0

Solution for 2y^2+5y-33=0 equation:

Simplifying
2y2 + 5y + -33 = 0

Reorder the terms:
-33 + 5y + 2y2 = 0

Solving
-33 + 5y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-11 + -2y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-11 + -2y)' equal to zero and attempt to solve:

Simplifying
-11 + -2y = 0

Solving
-11 + -2y = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2y = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2y = 0 + 11
-2y = 0 + 11

Combine like terms: 0 + 11 = 11
-2y = 11

Divide each side by '-2'.
y = -5.5

Simplifying
y = -5.5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5.5, 3}