7n^2-21n+3n-9=0

Solution for 7n^2-21n+3n-9=0 equation:

Simplifying
7n2 + -21n + 3n + -9 = 0

Reorder the terms:
-9 + -21n + 3n + 7n2 = 0

Combine like terms: -21n + 3n = -18n
-9 + -18n + 7n2 = 0

Solving
-9 + -18n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -7n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -7n)' equal to zero and attempt to solve:

Simplifying
-3 + -7n = 0

Solving
-3 + -7n = 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 + -7n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7n = 0 + 3
-7n = 0 + 3

Combine like terms: 0 + 3 = 3
-7n = 3

Divide each side by '-7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.4285714286, 3}