0.3(3n-5)=0.4-0.2(n-7)

Solution for 0.3(3n-5)=0.4-0.2(n-7) equation:

Simplifying
0.3(3n + -5) = 0.4 + -0.2(n + -7)

Reorder the terms:
0.3(-5 + 3n) = 0.4 + -0.2(n + -7)
(-5 * 0.3 + 3n * 0.3) = 0.4 + -0.2(n + -7)
(-1.5 + 0.9n) = 0.4 + -0.2(n + -7)

Reorder the terms:
-1.5 + 0.9n = 0.4 + -0.2(-7 + n)
-1.5 + 0.9n = 0.4 + (-7 * -0.2 + n * -0.2)
-1.5 + 0.9n = 0.4 + (1.4 + -0.2n)

Combine like terms: 0.4 + 1.4 = 1.8
-1.5 + 0.9n = 1.8 + -0.2n

Solving
-1.5 + 0.9n = 1.8 + -0.2n

Solving for variable 'n'.

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

Add '0.2n' to each side of the equation.
-1.5 + 0.9n + 0.2n = 1.8 + -0.2n + 0.2n

Combine like terms: 0.9n + 0.2n = 1.1n
-1.5 + 1.1n = 1.8 + -0.2n + 0.2n

Combine like terms: -0.2n + 0.2n = 0.0
-1.5 + 1.1n = 1.8 + 0.0
-1.5 + 1.1n = 1.8

Add '1.5' to each side of the equation.
-1.5 + 1.5 + 1.1n = 1.8 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.1n = 1.8 + 1.5
1.1n = 1.8 + 1.5

Combine like terms: 1.8 + 1.5 = 3.3
1.1n = 3.3

Divide each side by '1.1'.
n = 3

Simplifying
n = 3