(x+3)(x+1)=8

Solution for (x+3)(x+1)=8 equation:

Simplifying
(x + 3)(x + 1) = 8

Reorder the terms:
(3 + x)(x + 1) = 8

Reorder the terms:
(3 + x)(1 + x) = 8

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 8
((1 * 3 + x * 3) + x(1 + x)) = 8
((3 + 3x) + x(1 + x)) = 8
(3 + 3x + (1 * x + x * x)) = 8
(3 + 3x + (1x + x2)) = 8

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 8

Solving
3 + 4x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
3 + -8 + 4x + x2 = 8 + -8

Combine like terms: 3 + -8 = -5
-5 + 4x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-5 + 4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-5, 1}