(4y-6)(2y+4)=0

Solution for (4y-6)(2y+4)=0 equation:

Simplifying
(4y + -6)(2y + 4) = 0

Reorder the terms:
(-6 + 4y)(2y + 4) = 0

Reorder the terms:
(-6 + 4y)(4 + 2y) = 0

Multiply (-6 + 4y) * (4 + 2y)
(-6(4 + 2y) + 4y * (4 + 2y)) = 0
((4 * -6 + 2y * -6) + 4y * (4 + 2y)) = 0
((-24 + -12y) + 4y * (4 + 2y)) = 0
(-24 + -12y + (4 * 4y + 2y * 4y)) = 0
(-24 + -12y + (16y + 8y2)) = 0

Combine like terms: -12y + 16y = 4y
(-24 + 4y + 8y2) = 0

Solving
-24 + 4y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + y + 2y2) = 0

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

Ignore the factor 4.
Subproblem 1
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
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 = {-2, 1.5}