(4y-8)(y+3)=0

Solution for (4y-8)(y+3)=0 equation:

Simplifying
(4y + -8)(y + 3) = 0

Reorder the terms:
(-8 + 4y)(y + 3) = 0

Reorder the terms:
(-8 + 4y)(3 + y) = 0

Multiply (-8 + 4y) * (3 + y)
(-8(3 + y) + 4y * (3 + y)) = 0
((3 * -8 + y * -8) + 4y * (3 + y)) = 0
((-24 + -8y) + 4y * (3 + y)) = 0
(-24 + -8y + (3 * 4y + y * 4y)) = 0
(-24 + -8y + (12y + 4y2)) = 0

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

Solving
-24 + 4y + 4y2 = 0

Solving for variable 'y'.

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

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

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 2}