42n^2+9n=0

Solution for 42n^2+9n=0 equation:

Simplifying
42n2 + 9n = 0

Reorder the terms:
9n + 42n2 = 0

Solving
9n + 42n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(3 + 14n) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(3 + 14n)' equal to zero and attempt to solve:

Simplifying
3 + 14n = 0

Solving
3 + 14n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 14n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 14n = 0 + -3
14n = 0 + -3

Combine like terms: 0 + -3 = -3
14n = -3

Divide each side by '14'.
n = -0.2142857143

Simplifying
n = -0.2142857143
Solution
n = {0, -0.2142857143}