n^2-n=-3n^2-2n

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

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

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

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

Solving
-1n + n2 = -2n + -3n2

Solving for variable 'n'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + 4n) = 0

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 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

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

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

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {0, -0.25}