20n^2+88n+84n=0

Solution for 20n^2+88n+84n=0 equation:

Simplifying
20n2 + 88n + 84n = 0

Reorder the terms:
88n + 84n + 20n2 = 0

Combine like terms: 88n + 84n = 172n
172n + 20n2 = 0

Solving
172n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4n'.
4n(43 + 5n) = 0

Ignore the factor 4.
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 '(43 + 5n)' equal to zero and attempt to solve:

Simplifying
43 + 5n = 0

Solving
43 + 5n = 0

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

Add '-43' to each side of the equation.
43 + -43 + 5n = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 5n = 0 + -43
5n = 0 + -43

Combine like terms: 0 + -43 = -43
5n = -43

Divide each side by '5'.
n = -8.6

Simplifying
n = -8.6
Solution
n = {0, -8.6}