(6y+18)(4y-8)=0

Solution for (6y+18)(4y-8)=0 equation:

Simplifying
(6y + 18)(4y + -8) = 0

Reorder the terms:
(18 + 6y)(4y + -8) = 0

Reorder the terms:
(18 + 6y)(-8 + 4y) = 0

Multiply (18 + 6y) * (-8 + 4y)
(18(-8 + 4y) + 6y * (-8 + 4y)) = 0
((-8 * 18 + 4y * 18) + 6y * (-8 + 4y)) = 0
((-144 + 72y) + 6y * (-8 + 4y)) = 0
(-144 + 72y + (-8 * 6y + 4y * 6y)) = 0
(-144 + 72y + (-48y + 24y2)) = 0

Combine like terms: 72y + -48y = 24y
(-144 + 24y + 24y2) = 0

Solving
-144 + 24y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-6 + y + y2) = 0

Factor a trinomial.
24((-3 + -1y)(2 + -1y)) = 0

Ignore the factor 24.
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}