20y^2-13y-33=0

Solution for 20y^2-13y-33=0 equation:

Simplifying
20y2 + -13y + -33 = 0

Reorder the terms:
-33 + -13y + 20y2 = 0

Solving
-33 + -13y + 20y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(33 + -20y) = 0

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 '(33 + -20y)' equal to zero and attempt to solve:

Simplifying
33 + -20y = 0

Solving
33 + -20y = 0

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

Add '-33' to each side of the equation.
33 + -33 + -20y = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -20y = 0 + -33
-20y = 0 + -33

Combine like terms: 0 + -33 = -33
-20y = -33

Divide each side by '-20'.
y = 1.65

Simplifying
y = 1.65
Solution
y = {-1, 1.65}