(7n+1)(n-6)=0

Solution for (7n+1)(n-6)=0 equation:

Simplifying
(7n + 1)(n + -6) = 0

Reorder the terms:
(1 + 7n)(n + -6) = 0

Reorder the terms:
(1 + 7n)(-6 + n) = 0

Multiply (1 + 7n) * (-6 + n)
(1(-6 + n) + 7n * (-6 + n)) = 0
((-6 * 1 + n * 1) + 7n * (-6 + n)) = 0
((-6 + 1n) + 7n * (-6 + n)) = 0
(-6 + 1n + (-6 * 7n + n * 7n)) = 0
(-6 + 1n + (-42n + 7n2)) = 0

Combine like terms: 1n + -42n = -41n
(-6 + -41n + 7n2) = 0

Solving
-6 + -41n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -7n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

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