(4+y)(2y+9)=0

Solution for (4+y)(2y+9)=0 equation:

Simplifying
(4 + y)(2y + 9) = 0

Reorder the terms:
(4 + y)(9 + 2y) = 0

Multiply (4 + y) * (9 + 2y)
(4(9 + 2y) + y(9 + 2y)) = 0
((9 * 4 + 2y * 4) + y(9 + 2y)) = 0
((36 + 8y) + y(9 + 2y)) = 0
(36 + 8y + (9 * y + 2y * y)) = 0
(36 + 8y + (9y + 2y2)) = 0

Combine like terms: 8y + 9y = 17y
(36 + 17y + 2y2) = 0

Solving
36 + 17y + 2y2 = 0

Solving for variable 'y'.

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}