.2(a-5)-.1(3a+1)=0

Solution for .2(a-5)-.1(3a+1)=0 equation:

Simplifying
0.2(a + -5) + -0.1(3a + 1) = 0

Reorder the terms:
0.2(-5 + a) + -0.1(3a + 1) = 0
(-5 * 0.2 + a * 0.2) + -0.1(3a + 1) = 0
(-1 + 0.2a) + -0.1(3a + 1) = 0

Reorder the terms:
-1 + 0.2a + -0.1(1 + 3a) = 0
-1 + 0.2a + (1 * -0.1 + 3a * -0.1) = 0
-1 + 0.2a + (-0.1 + -0.3a) = 0

Reorder the terms:
-1 + -0.1 + 0.2a + -0.3a = 0

Combine like terms: -1 + -0.1 = -1.1
-1.1 + 0.2a + -0.3a = 0

Combine like terms: 0.2a + -0.3a = -0.1a
-1.1 + -0.1a = 0

Solving
-1.1 + -0.1a = 0

Solving for variable 'a'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + -0.1a = 0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + -0.1a = 0 + 1.1
-0.1a = 0 + 1.1

Combine like terms: 0 + 1.1 = 1.1
-0.1a = 1.1

Divide each side by '-0.1'.
a = -11

Simplifying
a = -11