2y^2+3y=90

Solution for 2y^2+3y=90 equation:

Simplifying
2y2 + 3y = 90

Reorder the terms:
3y + 2y2 = 90

Solving
3y + 2y2 = 90

Solving for variable 'y'.

Reorder the terms:
-90 + 3y + 2y2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 3y + 2y2 = 0

Factor a trinomial.
(-15 + -2y)(6 + -1y) = 0

Subproblem 1
Set the factor '(-15 + -2y)' equal to zero and attempt to solve:

Simplifying
-15 + -2y = 0

Solving
-15 + -2y = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2y = 0 + 15
-2y = 0 + 15

Combine like terms: 0 + 15 = 15
-2y = 15

Divide each side by '-2'.
y = -7.5

Simplifying
y = -7.5
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-7.5, 6}