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

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

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

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

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

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

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

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

Solving for variable 'n'.

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

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

Simplifying
-1 + -6n = 0

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

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

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

Divide each side by '-6'.
n = -0.1666666667

Simplifying
n = -0.1666666667
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-0.1666666667, 7}