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

Solution for (5-y)(4y-9)=0 equation:

Simplifying
(5 + -1y)(4y + -9) = 0

Reorder the terms:
(5 + -1y)(-9 + 4y) = 0

Multiply (5 + -1y) * (-9 + 4y)
(5(-9 + 4y) + -1y * (-9 + 4y)) = 0
((-9 * 5 + 4y * 5) + -1y * (-9 + 4y)) = 0
((-45 + 20y) + -1y * (-9 + 4y)) = 0
(-45 + 20y + (-9 * -1y + 4y * -1y)) = 0
(-45 + 20y + (9y + -4y2)) = 0

Combine like terms: 20y + 9y = 29y
(-45 + 29y + -4y2) = 0

Solving
-45 + 29y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + y)(9 + -4y) = 0

Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(9 + -4y)' equal to zero and attempt to solve:

Simplifying
9 + -4y = 0

Solving
9 + -4y = 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 + -4y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4y = 0 + -9
-4y = 0 + -9

Combine like terms: 0 + -9 = -9
-4y = -9

Divide each side by '-4'.
y = 2.25

Simplifying
y = 2.25
Solution
y = {5, 2.25}