13n^2+80n+128=5n^2

Solution for 13n^2+80n+128=5n^2 equation:

Simplifying
13n2 + 80n + 128 = 5n2

Reorder the terms:
128 + 80n + 13n2 = 5n2

Solving
128 + 80n + 13n2 = 5n2

Solving for variable 'n'.

Combine like terms: 13n2 + -5n2 = 8n2
128 + 80n + 8n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
128 + 80n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(16 + 10n + n2) = 0

Factor a trinomial.
8((8 + n)(2 + n)) = 0

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-8, -2}