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

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


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

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

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

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

Combine like terms: 7n + -48n = -41n
(56 + -41n + -6n2) = 0

Solving
56 + -41n + -6n2 = 0

Solving for variable 'n'.

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

Simplifying
8 + n = 0

Solving
8 + n = 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 + n = 0 + -8

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

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

Simplifying
n = -8
Solution
n = {1.166666667, -8}

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