3(2z+25)-2(z-2)=78

Solution for 3(2z+25)-2(z-2)=78 equation:

Simplifying
3(2z + 25) + -2(z + -2) = 78

Reorder the terms:
3(25 + 2z) + -2(z + -2) = 78
(25 * 3 + 2z * 3) + -2(z + -2) = 78
(75 + 6z) + -2(z + -2) = 78

Reorder the terms:
75 + 6z + -2(-2 + z) = 78
75 + 6z + (-2 * -2 + z * -2) = 78
75 + 6z + (4 + -2z) = 78

Reorder the terms:
75 + 4 + 6z + -2z = 78

Combine like terms: 75 + 4 = 79
79 + 6z + -2z = 78

Combine like terms: 6z + -2z = 4z
79 + 4z = 78

Solving
79 + 4z = 78

Solving for variable 'z'.

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

Add '-79' to each side of the equation.
79 + -79 + 4z = 78 + -79

Combine like terms: 79 + -79 = 0
0 + 4z = 78 + -79
4z = 78 + -79

Combine like terms: 78 + -79 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25