3(z+2)=5(z-4)

Solution for 3(z+2)=5(z-4) equation:

Simplifying
3(z + 2) = 5(z + -4)

Reorder the terms:
3(2 + z) = 5(z + -4)
(2 * 3 + z * 3) = 5(z + -4)
(6 + 3z) = 5(z + -4)

Reorder the terms:
6 + 3z = 5(-4 + z)
6 + 3z = (-4 * 5 + z * 5)
6 + 3z = (-20 + 5z)

Solving
6 + 3z = -20 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
6 + 3z + -5z = -20 + 5z + -5z

Combine like terms: 3z + -5z = -2z
6 + -2z = -20 + 5z + -5z

Combine like terms: 5z + -5z = 0
6 + -2z = -20 + 0
6 + -2z = -20

Add '-6' to each side of the equation.
6 + -6 + -2z = -20 + -6

Combine like terms: 6 + -6 = 0
0 + -2z = -20 + -6
-2z = -20 + -6

Combine like terms: -20 + -6 = -26
-2z = -26

Divide each side by '-2'.
z = 13

Simplifying
z = 13