24n^2+200n+64=0

Solution for 24n^2+200n+64=0 equation:

Simplifying
24n2 + 200n + 64 = 0

Reorder the terms:
64 + 200n + 24n2 = 0

Solving
64 + 200n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + 25n + 3n2) = 0

Factor a trinomial.
8((8 + n)(1 + 3n)) = 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 '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 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 + 3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3n = 0 + -1
3n = 0 + -1

Combine like terms: 0 + -1 = -1
3n = -1

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {-8, -0.3333333333}