-4(y+1)(-y+6)=0

Solution for -4(y+1)(-y+6)=0 equation:

Simplifying
-4(y + 1)(-1y + 6) = 0

Reorder the terms:
-4(1 + y)(-1y + 6) = 0

Reorder the terms:
-4(1 + y)(6 + -1y) = 0

Multiply (1 + y) * (6 + -1y)
-4(1(6 + -1y) + y(6 + -1y)) = 0
-4((6 * 1 + -1y * 1) + y(6 + -1y)) = 0
-4((6 + -1y) + y(6 + -1y)) = 0
-4(6 + -1y + (6 * y + -1y * y)) = 0
-4(6 + -1y + (6y + -1y2)) = 0

Combine like terms: -1y + 6y = 5y
-4(6 + 5y + -1y2) = 0
(6 * -4 + 5y * -4 + -1y2 * -4) = 0
(-24 + -20y + 4y2) = 0

Solving
-24 + -20y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -5y + y2) = 0

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

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
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 = {-1, 6}