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

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

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

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

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

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

Combine like terms: 1v + 3v = 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}