5n^2+50n+108=3

Solution for 5n^2+50n+108=3 equation:

Simplifying
5n2 + 50n + 108 = 3

Reorder the terms:
108 + 50n + 5n2 = 3

Solving
108 + 50n + 5n2 = 3

Solving for variable 'n'.

Reorder the terms:
108 + -3 + 50n + 5n2 = 3 + -3

Combine like terms: 108 + -3 = 105
105 + 50n + 5n2 = 3 + -3

Combine like terms: 3 + -3 = 0
105 + 50n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(21 + 10n + n2) = 0

Factor a trinomial.
5((7 + n)(3 + n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

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

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

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

Simplifying
n = -7
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

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

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

Simplifying
n = -3
Solution
n = {-7, -3}