v^2+12v+42=10

Solution for v^2+12v+42=10 equation:

Simplifying
v2 + 12v + 42 = 10

Reorder the terms:
42 + 12v + v2 = 10

Solving
42 + 12v + v2 = 10

Solving for variable 'v'.

Reorder the terms:
42 + -10 + 12v + v2 = 10 + -10

Combine like terms: 42 + -10 = 32
32 + 12v + v2 = 10 + -10

Combine like terms: 10 + -10 = 0
32 + 12v + v2 = 0

Factor a trinomial.
(8 + v)(4 + v) = 0

Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve:

Simplifying
8 + v = 0

Solving
8 + v = 0

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

Add '-8' to each side of the equation.
8 + -8 + v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + v = 0 + -8
v = 0 + -8

Combine like terms: 0 + -8 = -8
v = -8

Simplifying
v = -8
Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4
Solution
v = {-8, -4}