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

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

Simplifying
(6 + -1y)(2y + 9) = 0

Reorder the terms:
(6 + -1y)(9 + 2y) = 0

Multiply (6 + -1y) * (9 + 2y)
(6(9 + 2y) + -1y * (9 + 2y)) = 0
((9 * 6 + 2y * 6) + -1y * (9 + 2y)) = 0
((54 + 12y) + -1y * (9 + 2y)) = 0
(54 + 12y + (9 * -1y + 2y * -1y)) = 0
(54 + 12y + (-9y + -2y2)) = 0

Combine like terms: 12y + -9y = 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}