(3y-6)(4y-5)=0

Solution for (3y-6)(4y-5)=0 equation:

Simplifying
(3y + -6)(4y + -5) = 0

Reorder the terms:
(-6 + 3y)(4y + -5) = 0

Reorder the terms:
(-6 + 3y)(-5 + 4y) = 0

Multiply (-6 + 3y) * (-5 + 4y)
(-6(-5 + 4y) + 3y * (-5 + 4y)) = 0
((-5 * -6 + 4y * -6) + 3y * (-5 + 4y)) = 0
((30 + -24y) + 3y * (-5 + 4y)) = 0
(30 + -24y + (-5 * 3y + 4y * 3y)) = 0
(30 + -24y + (-15y + 12y2)) = 0

Combine like terms: -24y + -15y = -39y
(30 + -39y + 12y2) = 0

Solving
30 + -39y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -13y + 4y2) = 0

Factor a trinomial.
3((5 + -4y)(2 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -4y)' equal to zero and attempt to solve:

Simplifying
5 + -4y = 0

Solving
5 + -4y = 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 + -4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4y = 0 + -5
-4y = 0 + -5

Combine like terms: 0 + -5 = -5
-4y = -5

Divide each side by '-4'.
y = 1.25

Simplifying
y = 1.25
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {1.25, 2}