(n-5)(7n+1)=0

Solution for (n-5)(7n+1)=0 equation:

Simplifying
(n + -5)(7n + 1) = 0

Reorder the terms:
(-5 + n)(7n + 1) = 0

Reorder the terms:
(-5 + n)(1 + 7n) = 0

Multiply (-5 + n) * (1 + 7n)
(-5(1 + 7n) + n(1 + 7n)) = 0
((1 * -5 + 7n * -5) + n(1 + 7n)) = 0
((-5 + -35n) + n(1 + 7n)) = 0
(-5 + -35n + (1 * n + 7n * n)) = 0
(-5 + -35n + (1n + 7n2)) = 0

Combine like terms: -35n + 1n = -34n
(-5 + -34n + 7n2) = 0

Solving
-5 + -34n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -7n)(5 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-0.1428571429, 5}