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

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

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

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

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

Multiply (1 + x) * (-5 + x)
(1(-5 + x) + x(-5 + x)) = 16
((-5 * 1 + x * 1) + x(-5 + x)) = 16
((-5 + 1x) + x(-5 + x)) = 16
(-5 + 1x + (-5 * x + x * x)) = 16
(-5 + 1x + (-5x + x2)) = 16

Combine like terms: 1x + -5x = -4x
(-5 + -4x + x2) = 16

Solving
-5 + -4x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
-5 + -16 + -4x + x2 = 16 + -16

Combine like terms: -5 + -16 = -21
-21 + -4x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-21 + -4x + x2 = 0

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

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

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

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

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

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

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

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

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