8n(6n+7)=5

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}