3y(y-8)=-36

Solution for 3y(y-8)=-36 equation:

Simplifying
3y(y + -8) = -36

Reorder the terms:
3y(-8 + y) = -36
(-8 * 3y + y * 3y) = -36
(-24y + 3y2) = -36

Solving
-24y + 3y2 = -36

Solving for variable 'y'.

Reorder the terms:
36 + -24y + 3y2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -24y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8y + y2) = 0

Factor a trinomial.
3((2 + -1y)(6 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
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 = {2, 6}