-6n^2+3n-2=2-7n^2

Solution for -6n^2+3n-2=2-7n^2 equation:

Simplifying
-6n2 + 3n + -2 = 2 + -7n2

Reorder the terms:
-2 + 3n + -6n2 = 2 + -7n2

Solving
-2 + 3n + -6n2 = 2 + -7n2

Solving for variable 'n'.

Reorder the terms:
-2 + -2 + 3n + -6n2 + 7n2 = 2 + -7n2 + -2 + 7n2

Combine like terms: -2 + -2 = -4
-4 + 3n + -6n2 + 7n2 = 2 + -7n2 + -2 + 7n2

Combine like terms: -6n2 + 7n2 = 1n2
-4 + 3n + 1n2 = 2 + -7n2 + -2 + 7n2

Reorder the terms:
-4 + 3n + 1n2 = 2 + -2 + -7n2 + 7n2

Combine like terms: 2 + -2 = 0
-4 + 3n + 1n2 = 0 + -7n2 + 7n2
-4 + 3n + 1n2 = -7n2 + 7n2

Combine like terms: -7n2 + 7n2 = 0
-4 + 3n + 1n2 = 0

Factor a trinomial.
(-4 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

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

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

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
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
Solution
n = {-4, 1}