-0.1(n-13)=.9(n+.5)

Solution for -0.1(n-13)=.9(n+.5) equation:

Simplifying
-0.1(n + -13) = 0.9(n + 0.5)

Reorder the terms:
-0.1(-13 + n) = 0.9(n + 0.5)
(-13 * -0.1 + n * -0.1) = 0.9(n + 0.5)
(1.3 + -0.1n) = 0.9(n + 0.5)

Reorder the terms:
1.3 + -0.1n = 0.9(0.5 + n)
1.3 + -0.1n = (0.5 * 0.9 + n * 0.9)
1.3 + -0.1n = (0.45 + 0.9n)

Solving
1.3 + -0.1n = 0.45 + 0.9n

Solving for variable 'n'.

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

Add '-0.9n' to each side of the equation.
1.3 + -0.1n + -0.9n = 0.45 + 0.9n + -0.9n

Combine like terms: -0.1n + -0.9n = -1n
1.3 + -1n = 0.45 + 0.9n + -0.9n

Combine like terms: 0.9n + -0.9n = 0.0
1.3 + -1n = 0.45 + 0.0
1.3 + -1n = 0.45

Add '-1.3' to each side of the equation.
1.3 + -1.3 + -1n = 0.45 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + -1n = 0.45 + -1.3
-1n = 0.45 + -1.3

Combine like terms: 0.45 + -1.3 = -0.85
-1n = -0.85

Divide each side by '-1'.
n = 0.85

Simplifying
n = 0.85