(v+3)(v+1)=15

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

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

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

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

Multiply (3 + v) * (1 + v)
(3(1 + v) + v(1 + v)) = 15
((1 * 3 + v * 3) + v(1 + v)) = 15
((3 + 3v) + v(1 + v)) = 15
(3 + 3v + (1 * v + v * v)) = 15
(3 + 3v + (1v + v2)) = 15

Combine like terms: 3v + 1v = 4v
(3 + 4v + v2) = 15

Solving
3 + 4v + v2 = 15

Solving for variable 'v'.

Reorder the terms:
3 + -15 + 4v + v2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + 4v + v2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + 4v + v2 = 0

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

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

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

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

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

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

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

Simplifying
v = -6
Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

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

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

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

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

Simplifying
v = 2
Solution
v = {-6, 2}