50x^2n+145xn-360n=0

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Solution for 50x^2n+145xn-360n=0 equation: 


Simplifying
50x2n + 145xn + -360n = 0

Reorder the terms:
-360n + 145nx + 50nx2 = 0

Solving
-360n + 145nx + 50nx2 = 0

Solving for variable 'n'.

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

Factor out the Greatest Common Factor (GCF), '5n'.
5n(-72 + 29x + 10x2) = 0

Factor a trinomial.
5n((-9 + -2x)(8 + -5x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Add '2x' to each side of the equation.
-2x + 2x = 9 + 2x

Combine like terms: -2x + 2x = 0
0 = 9 + 2x

Simplifying
0 = 9 + 2x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Add '5x' to each side of the equation.
-5x + 5x = -8 + 5x

Combine like terms: -5x + 5x = 0
0 = -8 + 5x

Simplifying
0 = -8 + 5x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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