(2y-9)(6+y)=0

Solution for (2y-9)(6+y)=0 equation:

Simplifying
(2y + -9)(6 + y) = 0

Reorder the terms:
(-9 + 2y)(6 + y) = 0

Multiply (-9 + 2y) * (6 + y)
(-9(6 + y) + 2y * (6 + y)) = 0
((6 * -9 + y * -9) + 2y * (6 + y)) = 0
((-54 + -9y) + 2y * (6 + y)) = 0
(-54 + -9y + (6 * 2y + y * 2y)) = 0
(-54 + -9y + (12y + 2y2)) = 0

Combine like terms: -9y + 12y = 3y
(-54 + 3y + 2y2) = 0

Solving
-54 + 3y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(9 + -2y) = 0

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

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 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 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
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
Solution
y = {-6, 4.5}