(2n^4+n^3+n^2)-(n^3+7n^4+5n^2)=

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Solution for (2n^4+n^3+n^2)-(n^3+7n^4+5n^2)= equation: 


Simplifying
(2n4 + n3 + n2) + -1(n3 + 7n4 + 5n2) = 0

Reorder the terms:
(n2 + n3 + 2n4) + -1(n3 + 7n4 + 5n2) = 0

Remove parenthesis around (n2 + n3 + 2n4)
n2 + n3 + 2n4 + -1(n3 + 7n4 + 5n2) = 0

Reorder the terms:
n2 + n3 + 2n4 + -1(5n2 + n3 + 7n4) = 0
n2 + n3 + 2n4 + (5n2 * -1 + n3 * -1 + 7n4 * -1) = 0
n2 + n3 + 2n4 + (-5n2 + -1n3 + -7n4) = 0

Reorder the terms:
n2 + -5n2 + n3 + -1n3 + 2n4 + -7n4 = 0

Combine like terms: n2 + -5n2 = -4n2
-4n2 + n3 + -1n3 + 2n4 + -7n4 = 0

Combine like terms: n3 + -1n3 = 0
-4n2 + 0 + 2n4 + -7n4 = 0
-4n2 + 2n4 + -7n4 = 0

Combine like terms: 2n4 + -7n4 = -5n4
-4n2 + -5n4 = 0

Solving
-4n2 + -5n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1n2'.
-1n2(4 + 5n2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}

Subproblem 2
Set the factor '(4 + 5n2)' equal to zero and attempt to solve:

Simplifying
4 + 5n2 = 0

Solving
4 + 5n2 = 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 + 5n2 = 0 + -4

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

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

Divide each side by '5'.
n2 = -0.8

Simplifying
n2 = -0.8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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