7n^2=-42n

Solution for 7n^2=-42n equation:

Simplifying
7n2 = -42n

Solving
7n2 = -42n

Solving for variable 'n'.

Reorder the terms:
42n + 7n2 = -42n + 42n

Combine like terms: -42n + 42n = 0
42n + 7n2 = 0

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

Ignore the factor 7.
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 '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {0, -6}