5n^2+17n-9=3

Solution for 5n^2+17n-9=3 equation:

Simplifying
5n2 + 17n + -9 = 3

Reorder the terms:
-9 + 17n + 5n2 = 3

Solving
-9 + 17n + 5n2 = 3

Solving for variable 'n'.

Reorder the terms:
-9 + -3 + 17n + 5n2 = 3 + -3

Combine like terms: -9 + -3 = -12
-12 + 17n + 5n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-12 + 17n + 5n2 = 0

Factor a trinomial.
(-4 + -1n)(3 + -5n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 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 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {-4, 0.6}