(z+1)(z-5)-16=0

Solution for (z+1)(z-5)-16=0 equation:

Simplifying
(z + 1)(z + -5) + -16 = 0

Reorder the terms:
(1 + z)(z + -5) + -16 = 0

Reorder the terms:
(1 + z)(-5 + z) + -16 = 0

Multiply (1 + z) * (-5 + z)
(1(-5 + z) + z(-5 + z)) + -16 = 0
((-5 * 1 + z * 1) + z(-5 + z)) + -16 = 0
((-5 + 1z) + z(-5 + z)) + -16 = 0
(-5 + 1z + (-5 * z + z * z)) + -16 = 0
(-5 + 1z + (-5z + z2)) + -16 = 0

Combine like terms: 1z + -5z = -4z
(-5 + -4z + z2) + -16 = 0

Reorder the terms:
-5 + -16 + -4z + z2 = 0

Combine like terms: -5 + -16 = -21
-21 + -4z + z2 = 0

Solving
-21 + -4z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

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

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

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

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

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

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

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

Simplifying
z = 7
Solution
z = {-3, 7}