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

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

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

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

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

Multiply (7 + 6n) * (-6 + n)
(7(-6 + n) + 6n * (-6 + n)) = 0
((-6 * 7 + n * 7) + 6n * (-6 + n)) = 0
((-42 + 7n) + 6n * (-6 + n)) = 0
(-42 + 7n + (-6 * 6n + n * 6n)) = 0
(-42 + 7n + (-36n + 6n2)) = 0

Combine like terms: 7n + -36n = -29n
(-42 + -29n + 6n2) = 0

Solving
-42 + -29n + 6n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-7 + -6n = 0

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

Combine like terms: -7 + 7 = 0
0 + -6n = 0 + 7
-6n = 0 + 7

Combine like terms: 0 + 7 = 7
-6n = 7

Divide each side by '-6'.
n = -1.166666667

Simplifying
n = -1.166666667
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 = {-1.166666667, 6}