v(v+2)=15

Solution for v(v+2)=15 equation:

Simplifying
v(v + 2) = 15

Reorder the terms:
v(2 + v) = 15
(2 * v + v * v) = 15
(2v + v2) = 15

Solving
2v + v2 = 15

Solving for variable 'v'.

Reorder the terms:
-15 + 2v + v2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 2v + v2 = 0

Factor a trinomial.
(-5 + -1v)(3 + -1v) = 0

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

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

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

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

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

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

Simplifying
v = -5
Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-5, 3}