(2n+1)x(n-2)-(n+4)x(n-3)=0

Solution for (2n+1)x(n-2)-(n+4)x(n-3)=0 equation:

Simplifying
(2n + 1) * x(n + -2) + -1(n + 4) * x(n + -3) = 0

Reorder the terms:
(1 + 2n) * x(n + -2) + -1(n + 4) * x(n + -3) = 0

Reorder the terms:
(1 + 2n) * x(-2 + n) + -1(n + 4) * x(n + -3) = 0

Reorder the terms for easier multiplication:
x(1 + 2n)(-2 + n) + -1(n + 4) * x(n + -3) = 0

Multiply (1 + 2n) * (-2 + n)
x(1(-2 + n) + 2n * (-2 + n)) + -1(n + 4) * x(n + -3) = 0
x((-2 * 1 + n * 1) + 2n * (-2 + n)) + -1(n + 4) * x(n + -3) = 0
x((-2 + 1n) + 2n * (-2 + n)) + -1(n + 4) * x(n + -3) = 0
x(-2 + 1n + (-2 * 2n + n * 2n)) + -1(n + 4) * x(n + -3) = 0
x(-2 + 1n + (-4n + 2n2)) + -1(n + 4) * x(n + -3) = 0

Combine like terms: 1n + -4n = -3n
x(-2 + -3n + 2n2) + -1(n + 4) * x(n + -3) = 0
(-2 * x + -3n * x + 2n2 * x) + -1(n + 4) * x(n + -3) = 0

Reorder the terms:
(-3nx + 2n2x + -2x) + -1(n + 4) * x(n + -3) = 0
(-3nx + 2n2x + -2x) + -1(n + 4) * x(n + -3) = 0

Reorder the terms:
-3nx + 2n2x + -2x + -1(4 + n) * x(n + -3) = 0

Reorder the terms:
-3nx + 2n2x + -2x + -1(4 + n) * x(-3 + n) = 0

Reorder the terms for easier multiplication:
-3nx + 2n2x + -2x + -1x(4 + n)(-3 + n) = 0

Multiply (4 + n) * (-3 + n)
-3nx + 2n2x + -2x + -1x(4(-3 + n) + n(-3 + n)) = 0
-3nx + 2n2x + -2x + -1x((-3 * 4 + n * 4) + n(-3 + n)) = 0
-3nx + 2n2x + -2x + -1x((-12 + 4n) + n(-3 + n)) = 0
-3nx + 2n2x + -2x + -1x(-12 + 4n + (-3 * n + n * n)) = 0
-3nx + 2n2x + -2x + -1x(-12 + 4n + (-3n + n2)) = 0

Combine like terms: 4n + -3n = 1n
-3nx + 2n2x + -2x + -1x(-12 + 1n + n2) = 0
-3nx + 2n2x + -2x + (-12 * -1x + 1n * -1x + n2 * -1x) = 0

Reorder the terms:
-3nx + 2n2x + -2x + (-1nx + -1n2x + 12x) = 0
-3nx + 2n2x + -2x + (-1nx + -1n2x + 12x) = 0

Reorder the terms:
-3nx + -1nx + 2n2x + -1n2x + -2x + 12x = 0

Combine like terms: -3nx + -1nx = -4nx
-4nx + 2n2x + -1n2x + -2x + 12x = 0

Combine like terms: 2n2x + -1n2x = 1n2x
-4nx + 1n2x + -2x + 12x = 0

Combine like terms: -2x + 12x = 10x
-4nx + 1n2x + 10x = 0

Solving
-4nx + 1n2x + 10x = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4n + n2 + 10) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-4n + n2 + 10)' equal to zero and attempt to solve:

Simplifying
-4n + n2 + 10 = 0

Reorder the terms:
10 + -4n + n2 = 0

Solving
10 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -4n + -10 + n2 = 0 + -10

Reorder the terms:
10 + -10 + -4n + n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -4n + n2 = 0 + -10
-4n + n2 = 0 + -10

Combine like terms: 0 + -10 = -10
-4n + n2 = -10

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = -10 + 4

Reorder the terms:
4 + -4n + n2 = -10 + 4

Combine like terms: -10 + 4 = -6
4 + -4n + n2 = -6

Factor a perfect square on the left side:
(n + -2)(n + -2) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.