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

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

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

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

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

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

Combine like terms: -6y + 9y = 3y
(-54 + 3y + y2) = 0

Solving
-54 + 3y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-9, 6}