6n^2-5n-2=-4n+5n^2-2

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Solution for 6n^2-5n-2=-4n+5n^2-2 equation: 


Simplifying
6n2 + -5n + -2 = -4n + 5n2 + -2

Reorder the terms:
-2 + -5n + 6n2 = -4n + 5n2 + -2

Reorder the terms:
-2 + -5n + 6n2 = -2 + -4n + 5n2

Add '2' to each side of the equation.
-2 + -5n + 2 + 6n2 = -2 + -4n + 2 + 5n2

Reorder the terms:
-2 + 2 + -5n + 6n2 = -2 + -4n + 2 + 5n2

Combine like terms: -2 + 2 = 0
0 + -5n + 6n2 = -2 + -4n + 2 + 5n2
-5n + 6n2 = -2 + -4n + 2 + 5n2

Reorder the terms:
-5n + 6n2 = -2 + 2 + -4n + 5n2

Combine like terms: -2 + 2 = 0
-5n + 6n2 = 0 + -4n + 5n2
-5n + 6n2 = -4n + 5n2

Solving
-5n + 6n2 = -4n + 5n2

Solving for variable 'n'.

Reorder the terms:
-5n + 4n + 6n2 + -5n2 = -4n + 5n2 + 4n + -5n2

Combine like terms: -5n + 4n = -1n
-1n + 6n2 + -5n2 = -4n + 5n2 + 4n + -5n2

Combine like terms: 6n2 + -5n2 = 1n2
-1n + 1n2 = -4n + 5n2 + 4n + -5n2

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

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

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

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

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