v^2+15v+42=6+3v

Solution for v^2+15v+42=6+3v equation:

Simplifying
v2 + 15v + 42 = 6 + 3v

Reorder the terms:
42 + 15v + v2 = 6 + 3v

Solving
42 + 15v + v2 = 6 + 3v

Solving for variable 'v'.

Reorder the terms:
42 + -6 + 15v + -3v + v2 = 6 + 3v + -6 + -3v

Combine like terms: 42 + -6 = 36
36 + 15v + -3v + v2 = 6 + 3v + -6 + -3v

Combine like terms: 15v + -3v = 12v
36 + 12v + v2 = 6 + 3v + -6 + -3v

Reorder the terms:
36 + 12v + v2 = 6 + -6 + 3v + -3v

Combine like terms: 6 + -6 = 0
36 + 12v + v2 = 0 + 3v + -3v
36 + 12v + v2 = 3v + -3v

Combine like terms: 3v + -3v = 0
36 + 12v + v2 = 0

Factor a trinomial.
(6 + v)(6 + v) = 0

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

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

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

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

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

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

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

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

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