(x+1)(x+3)=323

Solution for (x+1)(x+3)=323 equation:

Simplifying
(x + 1)(x + 3) = 323

Reorder the terms:
(1 + x)(x + 3) = 323

Reorder the terms:
(1 + x)(3 + x) = 323

Multiply (1 + x) * (3 + x)
(1(3 + x) + x(3 + x)) = 323
((3 * 1 + x * 1) + x(3 + x)) = 323
((3 + 1x) + x(3 + x)) = 323
(3 + 1x + (3 * x + x * x)) = 323
(3 + 1x + (3x + x2)) = 323

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = 323

Solving
3 + 4x + x2 = 323

Solving for variable 'x'.

Reorder the terms:
3 + -323 + 4x + x2 = 323 + -323

Combine like terms: 3 + -323 = -320
-320 + 4x + x2 = 323 + -323

Combine like terms: 323 + -323 = 0
-320 + 4x + x2 = 0

Factor a trinomial.
(-20 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-20, 16}