0.1a+.6(200-a)=.5a(200)

Solution for 0.1a+.6(200-a)=.5a(200) equation:

Simplifying
0.1a + 0.6(200 + -1a) = 0.5a(200)
0.1a + (200 * 0.6 + -1a * 0.6) = 0.5a(200)
0.1a + (120 + -0.6a) = 0.5a(200)

Reorder the terms:
120 + 0.1a + -0.6a = 0.5a(200)

Combine like terms: 0.1a + -0.6a = -0.5a
120 + -0.5a = 0.5a(200)

Reorder the terms for easier multiplication:
120 + -0.5a = 0.5 * 200a

Multiply 0.5 * 200
120 + -0.5a = 100a

Solving
120 + -0.5a = 100a

Solving for variable 'a'.

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

Add '-100a' to each side of the equation.
120 + -0.5a + -100a = 100a + -100a

Combine like terms: -0.5a + -100a = -100.5a
120 + -100.5a = 100a + -100a

Combine like terms: 100a + -100a = 0
120 + -100.5a = 0

Add '-120' to each side of the equation.
120 + -120 + -100.5a = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -100.5a = 0 + -120
-100.5a = 0 + -120

Combine like terms: 0 + -120 = -120
-100.5a = -120

Divide each side by '-100.5'.
a = 1.194029851

Simplifying
a = 1.194029851