(4y+9)(6+y)=0

Solution for (4y+9)(6+y)=0 equation:

Simplifying
(4y + 9)(6 + y) = 0

Reorder the terms:
(9 + 4y)(6 + y) = 0

Multiply (9 + 4y) * (6 + y)
(9(6 + y) + 4y * (6 + y)) = 0
((6 * 9 + y * 9) + 4y * (6 + y)) = 0
((54 + 9y) + 4y * (6 + y)) = 0
(54 + 9y + (6 * 4y + y * 4y)) = 0
(54 + 9y + (24y + 4y2)) = 0

Combine like terms: 9y + 24y = 33y
(54 + 33y + 4y2) = 0

Solving
54 + 33y + 4y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Subproblem 2
Set the factor '(9 + 4y)' equal to zero and attempt to solve:

Simplifying
9 + 4y = 0

Solving
9 + 4y = 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 + 4y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4y = 0 + -9
4y = 0 + -9

Combine like terms: 0 + -9 = -9
4y = -9

Divide each side by '4'.
y = -2.25

Simplifying
y = -2.25
Solution
y = {-6, -2.25}