15n^2-50n-37=3

Solution for 15n^2-50n-37=3 equation:

Simplifying
15n2 + -50n + -37 = 3

Reorder the terms:
-37 + -50n + 15n2 = 3

Solving
-37 + -50n + 15n2 = 3

Solving for variable 'n'.

Reorder the terms:
-37 + -3 + -50n + 15n2 = 3 + -3

Combine like terms: -37 + -3 = -40
-40 + -50n + 15n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-40 + -50n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -10n + 3n2) = 0

Factor a trinomial.
5((-2 + -3n)(4 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -3n)' equal to zero and attempt to solve:

Simplifying
-2 + -3n = 0

Solving
-2 + -3n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3n = 0 + 2
-3n = 0 + 2

Combine like terms: 0 + 2 = 2
-3n = 2

Divide each side by '-3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-0.6666666667, 4}