42n^3+6n^2=0

Solution for 42n^3+6n^2=0 equation:

Simplifying
42n3 + 6n2 = 0

Reorder the terms:
6n2 + 42n3 = 0

Solving
6n2 + 42n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n2'.
6n2(1 + 7n) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
Subproblem 2
Set the factor '(1 + 7n)' equal to zero and attempt to solve:

Simplifying
1 + 7n = 0

Solving
1 + 7n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7n = 0 + -1
7n = 0 + -1

Combine like terms: 0 + -1 = -1
7n = -1

Divide each side by '7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Solution
n = {0, -0.1428571429}