7n(n+6)-8n(2-n)=

Solution for 7n(n+6)-8n(2-n)= equation:

Simplifying
7n(n + 6) + -8n(2 + -1n) = 0

Reorder the terms:
7n(6 + n) + -8n(2 + -1n) = 0
(6 * 7n + n * 7n) + -8n(2 + -1n) = 0
(42n + 7n2) + -8n(2 + -1n) = 0
42n + 7n2 + (2 * -8n + -1n * -8n) = 0
42n + 7n2 + (-16n + 8n2) = 0

Reorder the terms:
42n + -16n + 7n2 + 8n2 = 0

Combine like terms: 42n + -16n = 26n
26n + 7n2 + 8n2 = 0

Combine like terms: 7n2 + 8n2 = 15n2
26n + 15n2 = 0

Solving
26n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(26 + 15n) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(26 + 15n)' equal to zero and attempt to solve:

Simplifying
26 + 15n = 0

Solving
26 + 15n = 0

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

Add '-26' to each side of the equation.
26 + -26 + 15n = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 15n = 0 + -26
15n = 0 + -26

Combine like terms: 0 + -26 = -26
15n = -26

Divide each side by '15'.
n = -1.733333333

Simplifying
n = -1.733333333
Solution
n = {0, -1.733333333}