0.5(20n+2)+2(2.5+n)=0

Solution for 0.5(20n+2)+2(2.5+n)=0 equation:

Simplifying
0.5(20n + 2) + 2(2.5 + n) = 0

Reorder the terms:
0.5(2 + 20n) + 2(2.5 + n) = 0
(2 * 0.5 + 20n * 0.5) + 2(2.5 + n) = 0
(1 + 10n) + 2(2.5 + n) = 0
1 + 10n + (2.5 * 2 + n * 2) = 0
1 + 10n + (5 + 2n) = 0

Reorder the terms:
1 + 5 + 10n + 2n = 0

Combine like terms: 1 + 5 = 6
6 + 10n + 2n = 0

Combine like terms: 10n + 2n = 12n
6 + 12n = 0

Solving
6 + 12n = 0

Solving for variable 'n'.

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

Add '-6' to each side of the equation.
6 + -6 + 12n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12n = 0 + -6
12n = 0 + -6

Combine like terms: 0 + -6 = -6
12n = -6

Divide each side by '12'.
n = -0.5

Simplifying
n = -0.5