5z-3(z-4)+2(z-5)=30

Solution for 5z-3(z-4)+2(z-5)=30 equation:

Simplifying
5z + -3(z + -4) + 2(z + -5) = 30

Reorder the terms:
5z + -3(-4 + z) + 2(z + -5) = 30
5z + (-4 * -3 + z * -3) + 2(z + -5) = 30
5z + (12 + -3z) + 2(z + -5) = 30

Reorder the terms:
5z + 12 + -3z + 2(-5 + z) = 30
5z + 12 + -3z + (-5 * 2 + z * 2) = 30
5z + 12 + -3z + (-10 + 2z) = 30

Reorder the terms:
12 + -10 + 5z + -3z + 2z = 30

Combine like terms: 12 + -10 = 2
2 + 5z + -3z + 2z = 30

Combine like terms: 5z + -3z = 2z
2 + 2z + 2z = 30

Combine like terms: 2z + 2z = 4z
2 + 4z = 30

Solving
2 + 4z = 30

Solving for variable 'z'.

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

Add '-2' to each side of the equation.
2 + -2 + 4z = 30 + -2

Combine like terms: 2 + -2 = 0
0 + 4z = 30 + -2
4z = 30 + -2

Combine like terms: 30 + -2 = 28
4z = 28

Divide each side by '4'.
z = 7

Simplifying
z = 7