7N^2-N-6=0

Solution for 7N^2-N-6=0 equation:

Simplifying
7N2 + -1N + -6 = 0

Reorder the terms:
-6 + -1N + 7N2 = 0

Solving
-6 + -1N + 7N2 = 0

Solving for variable 'N'.

Factor a trinomial.
(-6 + -7N)(1 + -1N) = 0

Subproblem 1
Set the factor '(-6 + -7N)' equal to zero and attempt to solve:

Simplifying
-6 + -7N = 0

Solving
-6 + -7N = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7N = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7N = 0 + 6
-7N = 0 + 6

Combine like terms: 0 + 6 = 6
-7N = 6

Divide each side by '-7'.
N = -0.8571428571

Simplifying
N = -0.8571428571
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 = {-0.8571428571, 1}