(x-3)(x+1)=5

Solution for (x-3)(x+1)=5 equation:

Simplifying
(x + -3)(x + 1) = 5

Reorder the terms:
(-3 + x)(x + 1) = 5

Reorder the terms:
(-3 + x)(1 + x) = 5

Multiply (-3 + x) * (1 + x)
(-3(1 + x) + x(1 + x)) = 5
((1 * -3 + x * -3) + x(1 + x)) = 5
((-3 + -3x) + x(1 + x)) = 5
(-3 + -3x + (1 * x + x * x)) = 5
(-3 + -3x + (1x + x2)) = 5

Combine like terms: -3x + 1x = -2x
(-3 + -2x + x2) = 5

Solving
-3 + -2x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + -2x + x2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -2x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -2x + x2 = 0

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}