y(2y+17)=-36

Solution for y(2y+17)=-36 equation:

Simplifying
y(2y + 17) = -36

Reorder the terms:
y(17 + 2y) = -36
(17 * y + 2y * y) = -36
(17y + 2y2) = -36

Solving
17y + 2y2 = -36

Solving for variable 'y'.

Reorder the terms:
36 + 17y + 2y2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 17y + 2y2 = 0

Factor a trinomial.
(9 + 2y)(4 + y) = 0

Subproblem 1
Set the factor '(9 + 2y)' equal to zero and attempt to solve:

Simplifying
9 + 2y = 0

Solving
9 + 2y = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2y = 0 + -9

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

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

Divide each side by '2'.
y = -4.5

Simplifying
y = -4.5
Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

Simplifying
y = -4
Solution
y = {-4.5, -4}