10y^2=33y-20

Solution for 10y^2=33y-20 equation:

Simplifying
10y2 = 33y + -20

Reorder the terms:
10y2 = -20 + 33y

Solving
10y2 = -20 + 33y

Solving for variable 'y'.

Reorder the terms:
20 + -33y + 10y2 = -20 + 33y + 20 + -33y

Reorder the terms:
20 + -33y + 10y2 = -20 + 20 + 33y + -33y

Combine like terms: -20 + 20 = 0
20 + -33y + 10y2 = 0 + 33y + -33y
20 + -33y + 10y2 = 33y + -33y

Combine like terms: 33y + -33y = 0
20 + -33y + 10y2 = 0

Factor a trinomial.
(4 + -5y)(5 + -2y) = 0

Subproblem 1
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
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 = {0.8, 2.5}