3n^2-2n-7400=0

Solution for 3n^2-2n-7400=0 equation:

Simplifying
3n2 + -2n + -7400 = 0

Reorder the terms:
-7400 + -2n + 3n2 = 0

Solving
-7400 + -2n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-148 + -3n)(50 + -1n) = 0

Subproblem 1
Set the factor '(-148 + -3n)' equal to zero and attempt to solve:

Simplifying
-148 + -3n = 0

Solving
-148 + -3n = 0

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

Add '148' to each side of the equation.
-148 + 148 + -3n = 0 + 148

Combine like terms: -148 + 148 = 0
0 + -3n = 0 + 148
-3n = 0 + 148

Combine like terms: 0 + 148 = 148
-3n = 148

Divide each side by '-3'.
n = -49.33333333

Simplifying
n = -49.33333333
Subproblem 2
Set the factor '(50 + -1n)' equal to zero and attempt to solve:

Simplifying
50 + -1n = 0

Solving
50 + -1n = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1n = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1n = 0 + -50
-1n = 0 + -50

Combine like terms: 0 + -50 = -50
-1n = -50

Divide each side by '-1'.
n = 50

Simplifying
n = 50
Solution
n = {-49.33333333, 50}