.3(n+1)=.16(3n-5)

Solution for .3(n+1)=.16(3n-5) equation:

Simplifying
0.3(n + 1) = 0.16(3n + -5)

Reorder the terms:
0.3(1 + n) = 0.16(3n + -5)
(1 * 0.3 + n * 0.3) = 0.16(3n + -5)
(0.3 + 0.3n) = 0.16(3n + -5)

Reorder the terms:
0.3 + 0.3n = 0.16(-5 + 3n)
0.3 + 0.3n = (-5 * 0.16 + 3n * 0.16)
0.3 + 0.3n = (-0.8 + 0.48n)

Solving
0.3 + 0.3n = -0.8 + 0.48n

Solving for variable 'n'.

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

Add '-0.48n' to each side of the equation.
0.3 + 0.3n + -0.48n = -0.8 + 0.48n + -0.48n

Combine like terms: 0.3n + -0.48n = -0.18n
0.3 + -0.18n = -0.8 + 0.48n + -0.48n

Combine like terms: 0.48n + -0.48n = 0.00
0.3 + -0.18n = -0.8 + 0.00
0.3 + -0.18n = -0.8

Add '-0.3' to each side of the equation.
0.3 + -0.3 + -0.18n = -0.8 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -0.18n = -0.8 + -0.3
-0.18n = -0.8 + -0.3

Combine like terms: -0.8 + -0.3 = -1.1
-0.18n = -1.1

Divide each side by '-0.18'.
n = 6.111111111

Simplifying
n = 6.111111111