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

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

Simplifying
(4y + -6)(3 + -1y) = 0

Reorder the terms:
(-6 + 4y)(3 + -1y) = 0

Multiply (-6 + 4y) * (3 + -1y)
(-6(3 + -1y) + 4y * (3 + -1y)) = 0
((3 * -6 + -1y * -6) + 4y * (3 + -1y)) = 0
((-18 + 6y) + 4y * (3 + -1y)) = 0
(-18 + 6y + (3 * 4y + -1y * 4y)) = 0
(-18 + 6y + (12y + -4y2)) = 0

Combine like terms: 6y + 12y = 18y
(-18 + 18y + -4y2) = 0

Solving
-18 + 18y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 9y + -2y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + y)' equal to zero and attempt to solve:

Simplifying
-3 + y = 0

Solving
-3 + y = 0

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

Add '3' to each side of the equation.
-3 + 3 + y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + y = 0 + 3
y = 0 + 3

Combine like terms: 0 + 3 = 3
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {3, 1.5}