-7n^2-43n-6=0

Solution for -7n^2-43n-6=0 equation:

Simplifying
-7n2 + -43n + -6 = 0

Reorder the terms:
-6 + -43n + -7n2 = 0

Solving
-6 + -43n + -7n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 43n + 7n2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(1 + 7n)' equal to zero and attempt to solve:

Simplifying
1 + 7n = 0

Solving
1 + 7n = 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 + 7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7n = 0 + -1
7n = 0 + -1

Combine like terms: 0 + -1 = -1
7n = -1

Divide each side by '7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Solution
n = {-6, -0.1428571429}