2(z+3)+3(5-3z)=0

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

Simplifying
2(z + 3) + 3(5 + -3z) = 0

Reorder the terms:
2(3 + z) + 3(5 + -3z) = 0
(3 * 2 + z * 2) + 3(5 + -3z) = 0
(6 + 2z) + 3(5 + -3z) = 0
6 + 2z + (5 * 3 + -3z * 3) = 0
6 + 2z + (15 + -9z) = 0

Reorder the terms:
6 + 15 + 2z + -9z = 0

Combine like terms: 6 + 15 = 21
21 + 2z + -9z = 0

Combine like terms: 2z + -9z = -7z
21 + -7z = 0

Solving
21 + -7z = 0

Solving for variable 'z'.

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

Add '-21' to each side of the equation.
21 + -21 + -7z = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -7z = 0 + -21
-7z = 0 + -21

Combine like terms: 0 + -21 = -21
-7z = -21

Divide each side by '-7'.
z = 3

Simplifying
z = 3