1.5(a-3)-2(a-0.5)=10

Solution for 1.5(a-3)-2(a-0.5)=10 equation:

Simplifying
1.5(a + -3) + -2(a + -0.5) = 10

Reorder the terms:
1.5(-3 + a) + -2(a + -0.5) = 10
(-3 * 1.5 + a * 1.5) + -2(a + -0.5) = 10
(-4.5 + 1.5a) + -2(a + -0.5) = 10

Reorder the terms:
-4.5 + 1.5a + -2(-0.5 + a) = 10
-4.5 + 1.5a + (-0.5 * -2 + a * -2) = 10
-4.5 + 1.5a + (1 + -2a) = 10

Reorder the terms:
-4.5 + 1 + 1.5a + -2a = 10

Combine like terms: -4.5 + 1 = -3.5
-3.5 + 1.5a + -2a = 10

Combine like terms: 1.5a + -2a = -0.5a
-3.5 + -0.5a = 10

Solving
-3.5 + -0.5a = 10

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + -0.5a = 10 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -0.5a = 10 + 3.5
-0.5a = 10 + 3.5

Combine like terms: 10 + 3.5 = 13.5
-0.5a = 13.5

Divide each side by '-0.5'.
a = -27

Simplifying
a = -27