.1(x+40)-.08(x-20)=5.2

Solution for .1(x+40)-.08(x-20)=5.2 equation:

Simplifying
0.1(x + 40) + -0.08(x + -20) = 5.2

Reorder the terms:
0.1(40 + x) + -0.08(x + -20) = 5.2
(40 * 0.1 + x * 0.1) + -0.08(x + -20) = 5.2
(4 + 0.1x) + -0.08(x + -20) = 5.2

Reorder the terms:
4 + 0.1x + -0.08(-20 + x) = 5.2
4 + 0.1x + (-20 * -0.08 + x * -0.08) = 5.2
4 + 0.1x + (1.6 + -0.08x) = 5.2

Reorder the terms:
4 + 1.6 + 0.1x + -0.08x = 5.2

Combine like terms: 4 + 1.6 = 5.6
5.6 + 0.1x + -0.08x = 5.2

Combine like terms: 0.1x + -0.08x = 0.02x
5.6 + 0.02x = 5.2

Solving
5.6 + 0.02x = 5.2

Solving for variable 'x'.

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

Add '-5.6' to each side of the equation.
5.6 + -5.6 + 0.02x = 5.2 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
0.0 + 0.02x = 5.2 + -5.6
0.02x = 5.2 + -5.6

Combine like terms: 5.2 + -5.6 = -0.4
0.02x = -0.4

Divide each side by '0.02'.
x = -20

Simplifying
x = -20