(3y-6)*(8y-9)=0

Solution for (3y-6)*(8y-9)=0 equation:

Simplifying
(3y + -6)(8y + -9) = 0

Reorder the terms:
(-6 + 3y)(8y + -9) = 0

Reorder the terms:
(-6 + 3y)(-9 + 8y) = 0

Multiply (-6 + 3y) * (-9 + 8y)
(-6(-9 + 8y) + 3y * (-9 + 8y)) = 0
((-9 * -6 + 8y * -6) + 3y * (-9 + 8y)) = 0
((54 + -48y) + 3y * (-9 + 8y)) = 0
(54 + -48y + (-9 * 3y + 8y * 3y)) = 0
(54 + -48y + (-27y + 24y2)) = 0

Combine like terms: -48y + -27y = -75y
(54 + -75y + 24y2) = 0

Solving
54 + -75y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -25y + 8y2) = 0

Factor a trinomial.
3((9 + -8y)(2 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -8y)' equal to zero and attempt to solve:

Simplifying
9 + -8y = 0

Solving
9 + -8y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -8y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8y = 0 + -9
-8y = 0 + -9

Combine like terms: 0 + -9 = -9
-8y = -9

Divide each side by '-8'.
y = 1.125

Simplifying
y = 1.125
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 = {1.125, 2}