v^2+42v=0

Solution for v^2+42v=0 equation:

Simplifying
v2 + 42v = 0

Reorder the terms:
42v + v2 = 0

Solving
42v + v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), 'v'.
v(42 + v) = 0

Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0
Subproblem 2
Set the factor '(42 + v)' equal to zero and attempt to solve:

Simplifying
42 + v = 0

Solving
42 + v = 0

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

Add '-42' to each side of the equation.
42 + -42 + v = 0 + -42

Combine like terms: 42 + -42 = 0
0 + v = 0 + -42
v = 0 + -42

Combine like terms: 0 + -42 = -42
v = -42

Simplifying
v = -42
Solution
v = {0, -42}