=5n^2+17n+6

Solution for =5n^2+17n+6 equation:

Simplifying
0 = 5n2 + 17n + 6

Reorder the terms:
0 = 6 + 17n + 5n2

Solving
0 = 6 + 17n + 5n2

Solving for variable 'n'.

Combine like terms: 0 + -6 = -6
-6 + -17n + -5n2 = 6 + 17n + 5n2 + -6 + -17n + -5n2

Reorder the terms:
-6 + -17n + -5n2 = 6 + -6 + 17n + -17n + 5n2 + -5n2

Combine like terms: 6 + -6 = 0
-6 + -17n + -5n2 = 0 + 17n + -17n + 5n2 + -5n2
-6 + -17n + -5n2 = 17n + -17n + 5n2 + -5n2

Combine like terms: 17n + -17n = 0
-6 + -17n + -5n2 = 0 + 5n2 + -5n2
-6 + -17n + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
-6 + -17n + -5n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 17n + 5n2) = 0

Factor a trinomial.
-1((3 + n)(2 + 5n)) = 0

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-3, -0.4}