-3(y-7)(-y+6)=0

Solution for -3(y-7)(-y+6)=0 equation:

Simplifying
-3(y + -7)(-1y + 6) = 0

Reorder the terms:
-3(-7 + y)(-1y + 6) = 0

Reorder the terms:
-3(-7 + y)(6 + -1y) = 0

Multiply (-7 + y) * (6 + -1y)
-3(-7(6 + -1y) + y(6 + -1y)) = 0
-3((6 * -7 + -1y * -7) + y(6 + -1y)) = 0
-3((-42 + 7y) + y(6 + -1y)) = 0
-3(-42 + 7y + (6 * y + -1y * y)) = 0
-3(-42 + 7y + (6y + -1y2)) = 0

Combine like terms: 7y + 6y = 13y
-3(-42 + 13y + -1y2) = 0
(-42 * -3 + 13y * -3 + -1y2 * -3) = 0
(126 + -39y + 3y2) = 0

Solving
126 + -39y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + -13y + y2) = 0

Factor a trinomial.
3((6 + -1y)(7 + -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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {6, 7}