9n^2-2n-7=0

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

Simplifying
9n2 + -2n + -7 = 0

Reorder the terms:
-7 + -2n + 9n2 = 0

Solving
-7 + -2n + 9n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -9n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -9n)' equal to zero and attempt to solve:

Simplifying
-7 + -9n = 0

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

Combine like terms: -7 + 7 = 0
0 + -9n = 0 + 7
-9n = 0 + 7

Combine like terms: 0 + 7 = 7
-9n = 7

Divide each side by '-9'.
n = -0.7777777778

Simplifying
n = -0.7777777778
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Solution
n = {-0.7777777778, 1}