18n^2+69n+25=-5

Solution for 18n^2+69n+25=-5 equation:

Simplifying
18n2 + 69n + 25 = -5

Reorder the terms:
25 + 69n + 18n2 = -5

Solving
25 + 69n + 18n2 = -5

Solving for variable 'n'.

Reorder the terms:
25 + 5 + 69n + 18n2 = -5 + 5

Combine like terms: 25 + 5 = 30
30 + 69n + 18n2 = -5 + 5

Combine like terms: -5 + 5 = 0
30 + 69n + 18n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 23n + 6n2) = 0

Factor a trinomial.
3((10 + 3n)(1 + 2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(10 + 3n)' equal to zero and attempt to solve:

Simplifying
10 + 3n = 0

Solving
10 + 3n = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3n = 0 + -10
3n = 0 + -10

Combine like terms: 0 + -10 = -10
3n = -10

Divide each side by '3'.
n = -3.333333333

Simplifying
n = -3.333333333
Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {-3.333333333, -0.5}