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

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

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

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

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

Multiply (-3 + y) * (6 + y)
(-3(6 + y) + y(6 + y)) = 0
((6 * -3 + y * -3) + y(6 + y)) = 0
((-18 + -3y) + y(6 + y)) = 0
(-18 + -3y + (6 * y + y * y)) = 0
(-18 + -3y + (6y + y2)) = 0

Combine like terms: -3y + 6y = 3y
(-18 + 3y + y2) = 0

Solving
-18 + 3y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(3 + -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 '(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
Solution
y = {-6, 3}