200n^2+37n-330=6-3n

Solution for 200n^2+37n-330=6-3n equation:

Simplifying
200n2 + 37n + -330 = 6 + -3n

Reorder the terms:
-330 + 37n + 200n2 = 6 + -3n

Solving
-330 + 37n + 200n2 = 6 + -3n

Solving for variable 'n'.

Reorder the terms:
-330 + -6 + 37n + 3n + 200n2 = 6 + -3n + -6 + 3n

Combine like terms: -330 + -6 = -336
-336 + 37n + 3n + 200n2 = 6 + -3n + -6 + 3n

Combine like terms: 37n + 3n = 40n
-336 + 40n + 200n2 = 6 + -3n + -6 + 3n

Reorder the terms:
-336 + 40n + 200n2 = 6 + -6 + -3n + 3n

Combine like terms: 6 + -6 = 0
-336 + 40n + 200n2 = 0 + -3n + 3n
-336 + 40n + 200n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
-336 + 40n + 200n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-42 + 5n + 25n2) = 0

Factor a trinomial.
8((-7 + -5n)(6 + -5n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-7 + -5n)' equal to zero and attempt to solve:

Simplifying
-7 + -5n = 0

Solving
-7 + -5n = 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 + -5n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5n = 0 + 7
-5n = 0 + 7

Combine like terms: 0 + 7 = 7
-5n = 7

Divide each side by '-5'.
n = -1.4

Simplifying
n = -1.4
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 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 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-1.4, 1.2}