(y+1)(y-5)=16

Solution for (y+1)(y-5)=16 equation:

Simplifying
(y + 1)(y + -5) = 16

Reorder the terms:
(1 + y)(y + -5) = 16

Reorder the terms:
(1 + y)(-5 + y) = 16

Multiply (1 + y) * (-5 + y)
(1(-5 + y) + y(-5 + y)) = 16
((-5 * 1 + y * 1) + y(-5 + y)) = 16
((-5 + 1y) + y(-5 + y)) = 16
(-5 + 1y + (-5 * y + y * y)) = 16
(-5 + 1y + (-5y + y2)) = 16

Combine like terms: 1y + -5y = -4y
(-5 + -4y + y2) = 16

Solving
-5 + -4y + y2 = 16

Solving for variable 'y'.

Reorder the terms:
-5 + -16 + -4y + y2 = 16 + -16

Combine like terms: -5 + -16 = -21
-21 + -4y + y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-21 + -4y + y2 = 0

Factor a trinomial.
(-3 + -1y)(7 + -1y) = 0

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 7}