y(2y+9)=-9

Solution for y(2y+9)=-9 equation:

Simplifying
y(2y + 9) = -9

Reorder the terms:
y(9 + 2y) = -9
(9 * y + 2y * y) = -9
(9y + 2y2) = -9

Solving
9y + 2y2 = -9

Solving for variable 'y'.

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

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

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

Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-3, -1.5}