(4y-9)(6-y)=0

Solution for (4y-9)(6-y)=0 equation:

Simplifying
(4y + -9)(6 + -1y) = 0

Reorder the terms:
(-9 + 4y)(6 + -1y) = 0

Multiply (-9 + 4y) * (6 + -1y)
(-9(6 + -1y) + 4y * (6 + -1y)) = 0
((6 * -9 + -1y * -9) + 4y * (6 + -1y)) = 0
((-54 + 9y) + 4y * (6 + -1y)) = 0
(-54 + 9y + (6 * 4y + -1y * 4y)) = 0
(-54 + 9y + (24y + -4y2)) = 0

Combine like terms: 9y + 24y = 33y
(-54 + 33y + -4y2) = 0

Solving
-54 + 33y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(9 + -4y) = 0

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

Simplifying
-6 + y = 0

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

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

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

Simplifying
y = 6
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 = {6, 2.25}