10(z+3)-3(z-3)=2(z-1)+4(z-1)

Solution for 10(z+3)-3(z-3)=2(z-1)+4(z-1) equation:

Simplifying
10(z + 3) + -3(z + -3) = 2(z + -1) + 4(z + -1)

Reorder the terms:
10(3 + z) + -3(z + -3) = 2(z + -1) + 4(z + -1)
(3 * 10 + z * 10) + -3(z + -3) = 2(z + -1) + 4(z + -1)
(30 + 10z) + -3(z + -3) = 2(z + -1) + 4(z + -1)

Reorder the terms:
30 + 10z + -3(-3 + z) = 2(z + -1) + 4(z + -1)
30 + 10z + (-3 * -3 + z * -3) = 2(z + -1) + 4(z + -1)
30 + 10z + (9 + -3z) = 2(z + -1) + 4(z + -1)

Reorder the terms:
30 + 9 + 10z + -3z = 2(z + -1) + 4(z + -1)

Combine like terms: 30 + 9 = 39
39 + 10z + -3z = 2(z + -1) + 4(z + -1)

Combine like terms: 10z + -3z = 7z
39 + 7z = 2(z + -1) + 4(z + -1)

Reorder the terms:
39 + 7z = 2(-1 + z) + 4(z + -1)
39 + 7z = (-1 * 2 + z * 2) + 4(z + -1)
39 + 7z = (-2 + 2z) + 4(z + -1)

Reorder the terms:
39 + 7z = -2 + 2z + 4(-1 + z)
39 + 7z = -2 + 2z + (-1 * 4 + z * 4)
39 + 7z = -2 + 2z + (-4 + 4z)

Reorder the terms:
39 + 7z = -2 + -4 + 2z + 4z

Combine like terms: -2 + -4 = -6
39 + 7z = -6 + 2z + 4z

Combine like terms: 2z + 4z = 6z
39 + 7z = -6 + 6z

Solving
39 + 7z = -6 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
39 + 7z + -6z = -6 + 6z + -6z

Combine like terms: 7z + -6z = 1z
39 + 1z = -6 + 6z + -6z

Combine like terms: 6z + -6z = 0
39 + 1z = -6 + 0
39 + 1z = -6

Add '-39' to each side of the equation.
39 + -39 + 1z = -6 + -39

Combine like terms: 39 + -39 = 0
0 + 1z = -6 + -39
1z = -6 + -39

Combine like terms: -6 + -39 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45