(y-12)(y+6)=0

Solution for (y-12)(y+6)=0 equation:

Simplifying
(y + -12)(y + 6) = 0

Reorder the terms:
(-12 + y)(y + 6) = 0

Reorder the terms:
(-12 + y)(6 + y) = 0

Multiply (-12 + y) * (6 + y)
(-12(6 + y) + y(6 + y)) = 0
((6 * -12 + y * -12) + y(6 + y)) = 0
((-72 + -12y) + y(6 + y)) = 0
(-72 + -12y + (6 * y + y * y)) = 0
(-72 + -12y + (6y + y2)) = 0

Combine like terms: -12y + 6y = -6y
(-72 + -6y + y2) = 0

Solving
-72 + -6y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(12 + -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 '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y = 0 + -12
-1y = 0 + -12

Combine like terms: 0 + -12 = -12
-1y = -12

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Solution
y = {-6, 12}