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

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

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

Reorder the terms:
10(4 + z) + -1(4z + -2) = 3(z + -1) + 2(z + -3)
(4 * 10 + z * 10) + -1(4z + -2) = 3(z + -1) + 2(z + -3)
(40 + 10z) + -1(4z + -2) = 3(z + -1) + 2(z + -3)

Reorder the terms:
40 + 10z + -1(-2 + 4z) = 3(z + -1) + 2(z + -3)
40 + 10z + (-2 * -1 + 4z * -1) = 3(z + -1) + 2(z + -3)
40 + 10z + (2 + -4z) = 3(z + -1) + 2(z + -3)

Reorder the terms:
40 + 2 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 40 + 2 = 42
42 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 10z + -4z = 6z
42 + 6z = 3(z + -1) + 2(z + -3)

Reorder the terms:
42 + 6z = 3(-1 + z) + 2(z + -3)
42 + 6z = (-1 * 3 + z * 3) + 2(z + -3)
42 + 6z = (-3 + 3z) + 2(z + -3)

Reorder the terms:
42 + 6z = -3 + 3z + 2(-3 + z)
42 + 6z = -3 + 3z + (-3 * 2 + z * 2)
42 + 6z = -3 + 3z + (-6 + 2z)

Reorder the terms:
42 + 6z = -3 + -6 + 3z + 2z

Combine like terms: -3 + -6 = -9
42 + 6z = -9 + 3z + 2z

Combine like terms: 3z + 2z = 5z
42 + 6z = -9 + 5z

Solving
42 + 6z = -9 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
42 + 6z + -5z = -9 + 5z + -5z

Combine like terms: 6z + -5z = 1z
42 + 1z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
42 + 1z = -9 + 0
42 + 1z = -9

Add '-42' to each side of the equation.
42 + -42 + 1z = -9 + -42

Combine like terms: 42 + -42 = 0
0 + 1z = -9 + -42
1z = -9 + -42

Combine like terms: -9 + -42 = -51
1z = -51

Divide each side by '1'.
z = -51

Simplifying
z = -51