5n^2-1=3n-1+2n^2

Solution for 5n^2-1=3n-1+2n^2 equation:

Simplifying
5n2 + -1 = 3n + -1 + 2n2

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

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

Add '1' to each side of the equation.
-1 + 1 + 5n2 = -1 + 3n + 1 + 2n2

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

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

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

Solving
5n2 = 3n + 2n2

Solving for variable 'n'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-1 + n) = 0

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

Simplifying
-1 + n = 0

Solving
-1 + n = 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 + n = 0 + 1

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

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

Simplifying
n = 1
Solution
n = {0, 1}