5n^2+60n+154=-6

Solution for 5n^2+60n+154=-6 equation:

Simplifying
5n2 + 60n + 154 = -6

Reorder the terms:
154 + 60n + 5n2 = -6

Solving
154 + 60n + 5n2 = -6

Solving for variable 'n'.

Reorder the terms:
154 + 6 + 60n + 5n2 = -6 + 6

Combine like terms: 154 + 6 = 160
160 + 60n + 5n2 = -6 + 6

Combine like terms: -6 + 6 = 0
160 + 60n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(32 + 12n + n2) = 0

Factor a trinomial.
5((8 + n)(4 + n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-8, -4}