10n^2+2n=5n^2-2n

Solution for 10n^2+2n=5n^2-2n equation:

Simplifying
10n2 + 2n = 5n2 + -2n

Reorder the terms:
2n + 10n2 = 5n2 + -2n

Reorder the terms:
2n + 10n2 = -2n + 5n2

Solving
2n + 10n2 = -2n + 5n2

Solving for variable 'n'.

Reorder the terms:
2n + 2n + 10n2 + -5n2 = -2n + 5n2 + 2n + -5n2

Combine like terms: 2n + 2n = 4n
4n + 10n2 + -5n2 = -2n + 5n2 + 2n + -5n2

Combine like terms: 10n2 + -5n2 = 5n2
4n + 5n2 = -2n + 5n2 + 2n + -5n2

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(4 + 5n) = 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 '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 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 + 5n = 0 + -4

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

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

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

Simplifying
n = -0.8
Solution
n = {0, -0.8}