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

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

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

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

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

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

Solving for variable 'n'.

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

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

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

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

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

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

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

Simplifying
1 + -1n = 0

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

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

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

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

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

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

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

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

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Solution
n = {1, -1.5}