2(a-3)+3(a-2)=5

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

Simplifying
2(a + -3) + 3(a + -2) = 5

Reorder the terms:
2(-3 + a) + 3(a + -2) = 5
(-3 * 2 + a * 2) + 3(a + -2) = 5
(-6 + 2a) + 3(a + -2) = 5

Reorder the terms:
-6 + 2a + 3(-2 + a) = 5
-6 + 2a + (-2 * 3 + a * 3) = 5
-6 + 2a + (-6 + 3a) = 5

Reorder the terms:
-6 + -6 + 2a + 3a = 5

Combine like terms: -6 + -6 = -12
-12 + 2a + 3a = 5

Combine like terms: 2a + 3a = 5a
-12 + 5a = 5

Solving
-12 + 5a = 5

Solving for variable 'a'.

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

Add '12' to each side of the equation.
-12 + 12 + 5a = 5 + 12

Combine like terms: -12 + 12 = 0
0 + 5a = 5 + 12
5a = 5 + 12

Combine like terms: 5 + 12 = 17
5a = 17

Divide each side by '5'.
a = 3.4

Simplifying
a = 3.4