(3y-6)*(8y-6)=0

Solution for (3y-6)*(8y-6)=0 equation:

Simplifying
(3y + -6)(8y + -6) = 0

Reorder the terms:
(-6 + 3y)(8y + -6) = 0

Reorder the terms:
(-6 + 3y)(-6 + 8y) = 0

Multiply (-6 + 3y) * (-6 + 8y)
(-6(-6 + 8y) + 3y * (-6 + 8y)) = 0
((-6 * -6 + 8y * -6) + 3y * (-6 + 8y)) = 0
((36 + -48y) + 3y * (-6 + 8y)) = 0
(36 + -48y + (-6 * 3y + 8y * 3y)) = 0
(36 + -48y + (-18y + 24y2)) = 0

Combine like terms: -48y + -18y = -66y
(36 + -66y + 24y2) = 0

Solving
36 + -66y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -11y + 4y2) = 0

Factor a trinomial.
6((3 + -4y)(2 + -1y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 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 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
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 = {0.75, 2}