n^3-n^2+n=n^3+n^2-4n-3

Solution for n^3-n^2+n=n^3+n^2-4n-3 equation:

Simplifying
n3 + -1n2 + n = n3 + n2 + -4n + -3

Reorder the terms:
n + -1n2 + n3 = n3 + n2 + -4n + -3

Reorder the terms:
n + -1n2 + n3 = -3 + -4n + n2 + n3

Add '-1n3' to each side of the equation.
n + -1n2 + n3 + -1n3 = -3 + -4n + n2 + n3 + -1n3

Combine like terms: n3 + -1n3 = 0
n + -1n2 + 0 = -3 + -4n + n2 + n3 + -1n3
n + -1n2 = -3 + -4n + n2 + n3 + -1n3

Combine like terms: n3 + -1n3 = 0
n + -1n2 = -3 + -4n + n2 + 0
n + -1n2 = -3 + -4n + n2

Solving
n + -1n2 = -3 + -4n + n2

Solving for variable 'n'.

Reorder the terms:
3 + n + 4n + -1n2 + -1n2 = -3 + -4n + n2 + 3 + 4n + -1n2

Combine like terms: n + 4n = 5n
3 + 5n + -1n2 + -1n2 = -3 + -4n + n2 + 3 + 4n + -1n2

Combine like terms: -1n2 + -1n2 = -2n2
3 + 5n + -2n2 = -3 + -4n + n2 + 3 + 4n + -1n2

Reorder the terms:
3 + 5n + -2n2 = -3 + 3 + -4n + 4n + n2 + -1n2

Combine like terms: -3 + 3 = 0
3 + 5n + -2n2 = 0 + -4n + 4n + n2 + -1n2
3 + 5n + -2n2 = -4n + 4n + n2 + -1n2

Combine like terms: -4n + 4n = 0
3 + 5n + -2n2 = 0 + n2 + -1n2
3 + 5n + -2n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
3 + 5n + -2n2 = 0

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

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {3, -0.5}