(2y-9)(4-y)=0

Solution for (2y-9)(4-y)=0 equation:

Simplifying
(2y + -9)(4 + -1y) = 0

Reorder the terms:
(-9 + 2y)(4 + -1y) = 0

Multiply (-9 + 2y) * (4 + -1y)
(-9(4 + -1y) + 2y * (4 + -1y)) = 0
((4 * -9 + -1y * -9) + 2y * (4 + -1y)) = 0
((-36 + 9y) + 2y * (4 + -1y)) = 0
(-36 + 9y + (4 * 2y + -1y * 2y)) = 0
(-36 + 9y + (8y + -2y2)) = 0

Combine like terms: 9y + 8y = 17y
(-36 + 17y + -2y2) = 0

Solving
-36 + 17y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + 2y)(4 + -1y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {4.5, 4}