(y+9)(2y-3)=0

Solution for (y+9)(2y-3)=0 equation:

Simplifying
(y + 9)(2y + -3) = 0

Reorder the terms:
(9 + y)(2y + -3) = 0

Reorder the terms:
(9 + y)(-3 + 2y) = 0

Multiply (9 + y) * (-3 + 2y)
(9(-3 + 2y) + y(-3 + 2y)) = 0
((-3 * 9 + 2y * 9) + y(-3 + 2y)) = 0
((-27 + 18y) + y(-3 + 2y)) = 0
(-27 + 18y + (-3 * y + 2y * y)) = 0
(-27 + 18y + (-3y + 2y2)) = 0

Combine like terms: 18y + -3y = 15y
(-27 + 15y + 2y2) = 0

Solving
-27 + 15y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -1y)(3 + -2y) = 0

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

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 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 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
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 = {-9, 1.5}