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

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

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

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

Reorder the terms:
30 + 10z + -3(-2 + z) = 2(z + -1) + 4(z + -2)
30 + 10z + (-2 * -3 + z * -3) = 2(z + -1) + 4(z + -2)
30 + 10z + (6 + -3z) = 2(z + -1) + 4(z + -2)

Reorder the terms:
30 + 6 + 10z + -3z = 2(z + -1) + 4(z + -2)

Combine like terms: 30 + 6 = 36
36 + 10z + -3z = 2(z + -1) + 4(z + -2)

Combine like terms: 10z + -3z = 7z
36 + 7z = 2(z + -1) + 4(z + -2)

Reorder the terms:
36 + 7z = 2(-1 + z) + 4(z + -2)
36 + 7z = (-1 * 2 + z * 2) + 4(z + -2)
36 + 7z = (-2 + 2z) + 4(z + -2)

Reorder the terms:
36 + 7z = -2 + 2z + 4(-2 + z)
36 + 7z = -2 + 2z + (-2 * 4 + z * 4)
36 + 7z = -2 + 2z + (-8 + 4z)

Reorder the terms:
36 + 7z = -2 + -8 + 2z + 4z

Combine like terms: -2 + -8 = -10
36 + 7z = -10 + 2z + 4z

Combine like terms: 2z + 4z = 6z
36 + 7z = -10 + 6z

Solving
36 + 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.
36 + 7z + -6z = -10 + 6z + -6z

Combine like terms: 7z + -6z = 1z
36 + 1z = -10 + 6z + -6z

Combine like terms: 6z + -6z = 0
36 + 1z = -10 + 0
36 + 1z = -10

Add '-36' to each side of the equation.
36 + -36 + 1z = -10 + -36

Combine like terms: 36 + -36 = 0
0 + 1z = -10 + -36
1z = -10 + -36

Combine like terms: -10 + -36 = -46
1z = -46

Divide each side by '1'.
z = -46

Simplifying
z = -46