(-7n-1)(2n+1)=0

Solution for (-7n-1)(2n+1)=0 equation:

Simplifying
(-7n + -1)(2n + 1) = 0

Reorder the terms:
(-1 + -7n)(2n + 1) = 0

Reorder the terms:
(-1 + -7n)(1 + 2n) = 0

Multiply (-1 + -7n) * (1 + 2n)
(-1(1 + 2n) + -7n * (1 + 2n)) = 0
((1 * -1 + 2n * -1) + -7n * (1 + 2n)) = 0
((-1 + -2n) + -7n * (1 + 2n)) = 0
(-1 + -2n + (1 * -7n + 2n * -7n)) = 0
(-1 + -2n + (-7n + -14n2)) = 0

Combine like terms: -2n + -7n = -9n
(-1 + -9n + -14n2) = 0

Solving
-1 + -9n + -14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 9n + 14n2) = 0

Factor a trinomial.
-1((1 + 2n)(1 + 7n)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
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 = {-0.5, -0.1428571429}