.5(4n+6)=.25(16n-12)

Solution for .5(4n+6)=.25(16n-12) equation:

Simplifying
0.5(4n + 6) = 0.25(16n + -12)

Reorder the terms:
0.5(6 + 4n) = 0.25(16n + -12)
(6 * 0.5 + 4n * 0.5) = 0.25(16n + -12)
(3 + 2n) = 0.25(16n + -12)

Reorder the terms:
3 + 2n = 0.25(-12 + 16n)
3 + 2n = (-12 * 0.25 + 16n * 0.25)
3 + 2n = (-3 + 4n)

Solving
3 + 2n = -3 + 4n

Solving for variable 'n'.

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

Add '-4n' to each side of the equation.
3 + 2n + -4n = -3 + 4n + -4n

Combine like terms: 2n + -4n = -2n
3 + -2n = -3 + 4n + -4n

Combine like terms: 4n + -4n = 0
3 + -2n = -3 + 0
3 + -2n = -3

Add '-3' to each side of the equation.
3 + -3 + -2n = -3 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = -3 + -3
-2n = -3 + -3

Combine like terms: -3 + -3 = -6
-2n = -6

Divide each side by '-2'.
n = 3

Simplifying
n = 3