(8n-5)(6n+7)=0

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Solution for (8n-5)(6n+7)=0 equation: 


Simplifying
(8n + -5)(6n + 7) = 0

Reorder the terms:
(-5 + 8n)(6n + 7) = 0

Reorder the terms:
(-5 + 8n)(7 + 6n) = 0

Multiply (-5 + 8n) * (7 + 6n)
(-5(7 + 6n) + 8n * (7 + 6n)) = 0
((7 * -5 + 6n * -5) + 8n * (7 + 6n)) = 0
((-35 + -30n) + 8n * (7 + 6n)) = 0
(-35 + -30n + (7 * 8n + 6n * 8n)) = 0
(-35 + -30n + (56n + 48n2)) = 0

Combine like terms: -30n + 56n = 26n
(-35 + 26n + 48n2) = 0

Solving
-35 + 26n + 48n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -6n)(5 + -8n) = 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 '(5 + -8n)' equal to zero and attempt to solve:

Simplifying
5 + -8n = 0

Solving
5 + -8n = 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 + -8n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8n = 0 + -5
-8n = 0 + -5

Combine like terms: 0 + -5 = -5
-8n = -5

Divide each side by '-8'.
n = 0.625

Simplifying
n = 0.625
Solution
n = {-1.166666667, 0.625}

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