3(15-3y^2)+2y=5

Solution for 3(15-3y^2)+2y=5 equation:

Simplifying
3(15 + -3y2) + 2y = 5
(15 * 3 + -3y2 * 3) + 2y = 5
(45 + -9y2) + 2y = 5

Reorder the terms:
45 + 2y + -9y2 = 5

Solving
45 + 2y + -9y2 = 5

Solving for variable 'y'.

Reorder the terms:
45 + -5 + 2y + -9y2 = 5 + -5

Combine like terms: 45 + -5 = 40
40 + 2y + -9y2 = 5 + -5

Combine like terms: 5 + -5 = 0
40 + 2y + -9y2 = 0

Factor a trinomial.
(20 + -9y)(2 + y) = 0

Subproblem 1
Set the factor '(20 + -9y)' equal to zero and attempt to solve:

Simplifying
20 + -9y = 0

Solving
20 + -9y = 0

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

Add '-20' to each side of the equation.
20 + -20 + -9y = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -9y = 0 + -20
-9y = 0 + -20

Combine like terms: 0 + -20 = -20
-9y = -20

Divide each side by '-9'.
y = 2.222222222

Simplifying
y = 2.222222222
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {2.222222222, -2}