.33(n+1)=.166(3n-5)

Solution for .33(n+1)=.166(3n-5) equation:

Simplifying
0.33(n + 1) = 0.166(3n + -5)

Reorder the terms:
0.33(1 + n) = 0.166(3n + -5)
(1 * 0.33 + n * 0.33) = 0.166(3n + -5)
(0.33 + 0.33n) = 0.166(3n + -5)

Reorder the terms:
0.33 + 0.33n = 0.166(-5 + 3n)
0.33 + 0.33n = (-5 * 0.166 + 3n * 0.166)
0.33 + 0.33n = (-0.83 + 0.498n)

Solving
0.33 + 0.33n = -0.83 + 0.498n

Solving for variable 'n'.

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

Add '-0.498n' to each side of the equation.
0.33 + 0.33n + -0.498n = -0.83 + 0.498n + -0.498n

Combine like terms: 0.33n + -0.498n = -0.168n
0.33 + -0.168n = -0.83 + 0.498n + -0.498n

Combine like terms: 0.498n + -0.498n = 0.000
0.33 + -0.168n = -0.83 + 0.000
0.33 + -0.168n = -0.83

Add '-0.33' to each side of the equation.
0.33 + -0.33 + -0.168n = -0.83 + -0.33

Combine like terms: 0.33 + -0.33 = 0.00
0.00 + -0.168n = -0.83 + -0.33
-0.168n = -0.83 + -0.33

Combine like terms: -0.83 + -0.33 = -1.16
-0.168n = -1.16

Divide each side by '-0.168'.
n = 6.904761905

Simplifying
n = 6.904761905