(x+3)(x+1)=15

Solution for (x+3)(x+1)=15 equation:

Simplifying
(x + 3)(x + 1) = 15

Reorder the terms:
(3 + x)(x + 1) = 15

Reorder the terms:
(3 + x)(1 + x) = 15

Multiply (3 + x) * (1 + x)
(3(1 + x) + x(1 + x)) = 15
((1 * 3 + x * 3) + x(1 + x)) = 15
((3 + 3x) + x(1 + x)) = 15
(3 + 3x + (1 * x + x * x)) = 15
(3 + 3x + (1x + x2)) = 15

Combine like terms: 3x + 1x = 4x
(3 + 4x + x2) = 15

Solving
3 + 4x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
3 + -15 + 4x + x2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + 4x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 2}