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

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

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

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

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