2(a-3)+3(b-5)=0

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

Simplifying
2(a + -3) + 3(b + -5) = 0

Reorder the terms:
2(-3 + a) + 3(b + -5) = 0
(-3 * 2 + a * 2) + 3(b + -5) = 0
(-6 + 2a) + 3(b + -5) = 0

Reorder the terms:
-6 + 2a + 3(-5 + b) = 0
-6 + 2a + (-5 * 3 + b * 3) = 0
-6 + 2a + (-15 + 3b) = 0

Reorder the terms:
-6 + -15 + 2a + 3b = 0

Combine like terms: -6 + -15 = -21
-21 + 2a + 3b = 0

Solving
-21 + 2a + 3b = 0

Solving for variable 'a'.

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

Add '21' to each side of the equation.
-21 + 2a + 21 + 3b = 0 + 21

Reorder the terms:
-21 + 21 + 2a + 3b = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2a + 3b = 0 + 21
2a + 3b = 0 + 21

Combine like terms: 0 + 21 = 21
2a + 3b = 21

Add '-3b' to each side of the equation.
2a + 3b + -3b = 21 + -3b

Combine like terms: 3b + -3b = 0
2a + 0 = 21 + -3b
2a = 21 + -3b

Divide each side by '2'.
a = 10.5 + -1.5b

Simplifying
a = 10.5 + -1.5b