.5(2n-3)-0.1=0.4(6+2n)

Solution for .5(2n-3)-0.1=0.4(6+2n) equation:

Simplifying
0.5(2n + -3) + -0.1 = 0.4(6 + 2n)

Reorder the terms:
0.5(-3 + 2n) + -0.1 = 0.4(6 + 2n)
(-3 * 0.5 + 2n * 0.5) + -0.1 = 0.4(6 + 2n)
(-1.5 + 1n) + -0.1 = 0.4(6 + 2n)

Reorder the terms:
-1.5 + -0.1 + 1n = 0.4(6 + 2n)

Combine like terms: -1.5 + -0.1 = -1.6
-1.6 + 1n = 0.4(6 + 2n)
-1.6 + 1n = (6 * 0.4 + 2n * 0.4)
-1.6 + 1n = (2.4 + 0.8n)

Solving
-1.6 + 1n = 2.4 + 0.8n

Solving for variable 'n'.

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

Add '-0.8n' to each side of the equation.
-1.6 + 1n + -0.8n = 2.4 + 0.8n + -0.8n

Combine like terms: 1n + -0.8n = 0.2n
-1.6 + 0.2n = 2.4 + 0.8n + -0.8n

Combine like terms: 0.8n + -0.8n = 0.0
-1.6 + 0.2n = 2.4 + 0.0
-1.6 + 0.2n = 2.4

Add '1.6' to each side of the equation.
-1.6 + 1.6 + 0.2n = 2.4 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.2n = 2.4 + 1.6
0.2n = 2.4 + 1.6

Combine like terms: 2.4 + 1.6 = 4
0.2n = 4

Divide each side by '0.2'.
n = 20

Simplifying
n = 20