8n(6n+7)=5

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


Simplifying
8n(6n + 7) = 5

Reorder the terms:
8n(7 + 6n) = 5
(7 * 8n + 6n * 8n) = 5
(56n + 48n2) = 5

Solving
56n + 48n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + 56n + 48n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 56n + 48n2 = 0

Factor a trinomial.
(-5 + -4n)(1 + -12n) = 0

Subproblem 1

Set the factor '(-5 + -4n)' equal to zero and attempt to solve: Simplifying -5 + -4n = 0 Solving -5 + -4n = 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 + -4n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4n = 0 + 5 -4n = 0 + 5 Combine like terms: 0 + 5 = 5 -4n = 5 Divide each side by '-4'. n = -1.25 Simplifying n = -1.25

Subproblem 2

Set the factor '(1 + -12n)' equal to zero and attempt to solve: Simplifying 1 + -12n = 0 Solving 1 + -12n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -12n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12n = 0 + -1 -12n = 0 + -1 Combine like terms: 0 + -1 = -1 -12n = -1 Divide each side by '-12'. n = 0.08333333333 Simplifying n = 0.08333333333

Solution

n = {-1.25, 0.08333333333}

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