10n^2-6n-448=0

Solution for 10n^2-6n-448=0 equation:

Simplifying
10n2 + -6n + -448 = 0

Reorder the terms:
-448 + -6n + 10n2 = 0

Solving
-448 + -6n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-224 + -3n + 5n2) = 0

Factor a trinomial.
2((-32 + -5n)(7 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-32 + -5n)' equal to zero and attempt to solve:

Simplifying
-32 + -5n = 0

Solving
-32 + -5n = 0

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

Add '32' to each side of the equation.
-32 + 32 + -5n = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -5n = 0 + 32
-5n = 0 + 32

Combine like terms: 0 + 32 = 32
-5n = 32

Divide each side by '-5'.
n = -6.4

Simplifying
n = -6.4
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-6.4, 7}