3(y+8)(y-6)=-72

Solution for 3(y+8)(y-6)=-72 equation:

Simplifying
3(y + 8)(y + -6) = -72

Reorder the terms:
3(8 + y)(y + -6) = -72

Reorder the terms:
3(8 + y)(-6 + y) = -72

Multiply (8 + y) * (-6 + y)
3(8(-6 + y) + y(-6 + y)) = -72
3((-6 * 8 + y * 8) + y(-6 + y)) = -72
3((-48 + 8y) + y(-6 + y)) = -72
3(-48 + 8y + (-6 * y + y * y)) = -72
3(-48 + 8y + (-6y + y2)) = -72

Combine like terms: 8y + -6y = 2y
3(-48 + 2y + y2) = -72
(-48 * 3 + 2y * 3 + y2 * 3) = -72
(-144 + 6y + 3y2) = -72

Solving
-144 + 6y + 3y2 = -72

Solving for variable 'y'.

Reorder the terms:
-144 + 72 + 6y + 3y2 = -72 + 72

Combine like terms: -144 + 72 = -72
-72 + 6y + 3y2 = -72 + 72

Combine like terms: -72 + 72 = 0
-72 + 6y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 2y + y2) = 0

Factor a trinomial.
3((-6 + -1y)(4 + -1y)) = 0

Ignore the factor 3.
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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-6, 4}