.75(n+6)-.5(n-3)=0

Solution for .75(n+6)-.5(n-3)=0 equation:

Simplifying
0.75(n + 6) + -0.5(n + -3) = 0

Reorder the terms:
0.75(6 + n) + -0.5(n + -3) = 0
(6 * 0.75 + n * 0.75) + -0.5(n + -3) = 0
(4.5 + 0.75n) + -0.5(n + -3) = 0

Reorder the terms:
4.5 + 0.75n + -0.5(-3 + n) = 0
4.5 + 0.75n + (-3 * -0.5 + n * -0.5) = 0
4.5 + 0.75n + (1.5 + -0.5n) = 0

Reorder the terms:
4.5 + 1.5 + 0.75n + -0.5n = 0

Combine like terms: 4.5 + 1.5 = 6
6 + 0.75n + -0.5n = 0

Combine like terms: 0.75n + -0.5n = 0.25n
6 + 0.25n = 0

Solving
6 + 0.25n = 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 + 0.25n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 0.25n = 0 + -6
0.25n = 0 + -6

Combine like terms: 0 + -6 = -6
0.25n = -6

Divide each side by '0.25'.
n = -24

Simplifying
n = -24