(6n+7)(7n+8)=0

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Solution for (6n+7)(7n+8)=0 equation: 


Simplifying
(6n + 7)(7n + 8) = 0

Reorder the terms:
(7 + 6n)(7n + 8) = 0

Reorder the terms:
(7 + 6n)(8 + 7n) = 0

Multiply (7 + 6n) * (8 + 7n)
(7(8 + 7n) + 6n * (8 + 7n)) = 0
((8 * 7 + 7n * 7) + 6n * (8 + 7n)) = 0
((56 + 49n) + 6n * (8 + 7n)) = 0
(56 + 49n + (8 * 6n + 7n * 6n)) = 0
(56 + 49n + (48n + 42n2)) = 0

Combine like terms: 49n + 48n = 97n
(56 + 97n + 42n2) = 0

Solving
56 + 97n + 42n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + 6n)(8 + 7n) = 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 '(8 + 7n)' equal to zero and attempt to solve:

Simplifying
8 + 7n = 0

Solving
8 + 7n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7n = 0 + -8
7n = 0 + -8

Combine like terms: 0 + -8 = -8
7n = -8

Divide each side by '7'.
n = -1.142857143

Simplifying
n = -1.142857143
Solution
n = {-1.166666667, -1.142857143}

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