24n^2+200n+336=0

Solution for 24n^2+200n+336=0 equation:

Simplifying
24n2 + 200n + 336 = 0

Reorder the terms:
336 + 200n + 24n2 = 0

Solving
336 + 200n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(42 + 25n + 3n2) = 0

Factor a trinomial.
8((6 + n)(7 + 3n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(7 + 3n)' equal to zero and attempt to solve:

Simplifying
7 + 3n = 0

Solving
7 + 3n = 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 + 3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3n = 0 + -7
3n = 0 + -7

Combine like terms: 0 + -7 = -7
3n = -7

Divide each side by '3'.
n = -2.333333333

Simplifying
n = -2.333333333
Solution
n = {-6, -2.333333333}