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

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

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

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

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

Multiply (-6 + 7n) * (7 + n)
(-6(7 + n) + 7n * (7 + n)) = 0
((7 * -6 + n * -6) + 7n * (7 + n)) = 0
((-42 + -6n) + 7n * (7 + n)) = 0
(-42 + -6n + (7 * 7n + n * 7n)) = 0
(-42 + -6n + (49n + 7n2)) = 0

Combine like terms: -6n + 49n = 43n
(-42 + 43n + 7n2) = 0

Solving
-42 + 43n + 7n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

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

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

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

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Solution
n = {-7, 0.8571428571}