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

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

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

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

Reorder the terms:
30 + 10z + -3(-4 + z) = 4(z + -1) + 2(z + -2)
30 + 10z + (-4 * -3 + z * -3) = 4(z + -1) + 2(z + -2)
30 + 10z + (12 + -3z) = 4(z + -1) + 2(z + -2)

Reorder the terms:
30 + 12 + 10z + -3z = 4(z + -1) + 2(z + -2)

Combine like terms: 30 + 12 = 42
42 + 10z + -3z = 4(z + -1) + 2(z + -2)

Combine like terms: 10z + -3z = 7z
42 + 7z = 4(z + -1) + 2(z + -2)

Reorder the terms:
42 + 7z = 4(-1 + z) + 2(z + -2)
42 + 7z = (-1 * 4 + z * 4) + 2(z + -2)
42 + 7z = (-4 + 4z) + 2(z + -2)

Reorder the terms:
42 + 7z = -4 + 4z + 2(-2 + z)
42 + 7z = -4 + 4z + (-2 * 2 + z * 2)
42 + 7z = -4 + 4z + (-4 + 2z)

Reorder the terms:
42 + 7z = -4 + -4 + 4z + 2z

Combine like terms: -4 + -4 = -8
42 + 7z = -8 + 4z + 2z

Combine like terms: 4z + 2z = 6z
42 + 7z = -8 + 6z

Solving
42 + 7z = -8 + 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.
42 + 7z + -6z = -8 + 6z + -6z

Combine like terms: 7z + -6z = 1z
42 + 1z = -8 + 6z + -6z

Combine like terms: 6z + -6z = 0
42 + 1z = -8 + 0
42 + 1z = -8

Add '-42' to each side of the equation.
42 + -42 + 1z = -8 + -42

Combine like terms: 42 + -42 = 0
0 + 1z = -8 + -42
1z = -8 + -42

Combine like terms: -8 + -42 = -50
1z = -50

Divide each side by '1'.
z = -50

Simplifying
z = -50