1.5(2a+1)=5(0.5a+0.3)+0.1

Solution for 1.5(2a+1)=5(0.5a+0.3)+0.1 equation:

Simplifying
1.5(2a + 1) = 5(0.5a + 0.3) + 0.1

Reorder the terms:
1.5(1 + 2a) = 5(0.5a + 0.3) + 0.1
(1 * 1.5 + 2a * 1.5) = 5(0.5a + 0.3) + 0.1
(1.5 + 3a) = 5(0.5a + 0.3) + 0.1

Reorder the terms:
1.5 + 3a = 5(0.3 + 0.5a) + 0.1
1.5 + 3a = (0.3 * 5 + 0.5a * 5) + 0.1
1.5 + 3a = (1.5 + 2.5a) + 0.1

Reorder the terms:
1.5 + 3a = 1.5 + 0.1 + 2.5a

Combine like terms: 1.5 + 0.1 = 1.6
1.5 + 3a = 1.6 + 2.5a

Solving
1.5 + 3a = 1.6 + 2.5a

Solving for variable 'a'.

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

Add '-2.5a' to each side of the equation.
1.5 + 3a + -2.5a = 1.6 + 2.5a + -2.5a

Combine like terms: 3a + -2.5a = 0.5a
1.5 + 0.5a = 1.6 + 2.5a + -2.5a

Combine like terms: 2.5a + -2.5a = 0.0
1.5 + 0.5a = 1.6 + 0.0
1.5 + 0.5a = 1.6

Add '-1.5' to each side of the equation.
1.5 + -1.5 + 0.5a = 1.6 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5a = 1.6 + -1.5
0.5a = 1.6 + -1.5

Combine like terms: 1.6 + -1.5 = 0.1
0.5a = 0.1

Divide each side by '0.5'.
a = 0.2

Simplifying
a = 0.2