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

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


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

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

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

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

Combine like terms: -5x + 1x = -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}

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