(n+5)(6n+7)=0

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Solution for (n+5)(6n+7)=0 equation: 


Simplifying
(n + 5)(6n + 7) = 0

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

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

Multiply (5 + n) * (7 + 6n)
(5(7 + 6n) + n(7 + 6n)) = 0
((7 * 5 + 6n * 5) + n(7 + 6n)) = 0
((35 + 30n) + n(7 + 6n)) = 0
(35 + 30n + (7 * n + 6n * n)) = 0
(35 + 30n + (7n + 6n2)) = 0

Combine like terms: 30n + 7n = 37n
(35 + 37n + 6n2) = 0

Solving
35 + 37n + 6n2 = 0

Solving for variable 'n'.

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


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

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

Simplifying
n = -5

Subproblem 2
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
Solution
n = {-5, -1.166666667}

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