(y-9)(y-6)=0

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

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

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

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

Multiply (-9 + y) * (-6 + y)
(-9(-6 + y) + y(-6 + y)) = 0
((-6 * -9 + y * -9) + y(-6 + y)) = 0
((54 + -9y) + y(-6 + y)) = 0
(54 + -9y + (-6 * y + y * y)) = 0
(54 + -9y + (-6y + y2)) = 0

Combine like terms: -9y + -6y = -15y
(54 + -15y + y2) = 0

Solving
54 + -15y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + -1y)(9 + -1y) = 0

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

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 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 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {6, 9}