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

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

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

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

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

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

Combine like terms: 30 + 3 = 33
33 + 10z + -3z = 4(z + -1) + 2(z + -3)

Combine like terms: 10z + -3z = 7z
33 + 7z = 4(z + -1) + 2(z + -3)

Reorder the terms:
33 + 7z = 4(-1 + z) + 2(z + -3)
33 + 7z = (-1 * 4 + z * 4) + 2(z + -3)
33 + 7z = (-4 + 4z) + 2(z + -3)

Reorder the terms:
33 + 7z = -4 + 4z + 2(-3 + z)
33 + 7z = -4 + 4z + (-3 * 2 + z * 2)
33 + 7z = -4 + 4z + (-6 + 2z)

Reorder the terms:
33 + 7z = -4 + -6 + 4z + 2z

Combine like terms: -4 + -6 = -10
33 + 7z = -10 + 4z + 2z

Combine like terms: 4z + 2z = 6z
33 + 7z = -10 + 6z

Solving
33 + 7z = -10 + 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.
33 + 7z + -6z = -10 + 6z + -6z

Combine like terms: 7z + -6z = 1z
33 + 1z = -10 + 6z + -6z

Combine like terms: 6z + -6z = 0
33 + 1z = -10 + 0
33 + 1z = -10

Add '-33' to each side of the equation.
33 + -33 + 1z = -10 + -33

Combine like terms: 33 + -33 = 0
0 + 1z = -10 + -33
1z = -10 + -33

Combine like terms: -10 + -33 = -43
1z = -43

Divide each side by '1'.
z = -43

Simplifying
z = -43