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

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

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

Reorder the terms:
10(2 + z) + -3(z + -1) = 2(z + -2) + 4(z + -1)
(2 * 10 + z * 10) + -3(z + -1) = 2(z + -2) + 4(z + -1)
(20 + 10z) + -3(z + -1) = 2(z + -2) + 4(z + -1)

Reorder the terms:
20 + 10z + -3(-1 + z) = 2(z + -2) + 4(z + -1)
20 + 10z + (-1 * -3 + z * -3) = 2(z + -2) + 4(z + -1)
20 + 10z + (3 + -3z) = 2(z + -2) + 4(z + -1)

Reorder the terms:
20 + 3 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 20 + 3 = 23
23 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 10z + -3z = 7z
23 + 7z = 2(z + -2) + 4(z + -1)

Reorder the terms:
23 + 7z = 2(-2 + z) + 4(z + -1)
23 + 7z = (-2 * 2 + z * 2) + 4(z + -1)
23 + 7z = (-4 + 2z) + 4(z + -1)

Reorder the terms:
23 + 7z = -4 + 2z + 4(-1 + z)
23 + 7z = -4 + 2z + (-1 * 4 + z * 4)
23 + 7z = -4 + 2z + (-4 + 4z)

Reorder the terms:
23 + 7z = -4 + -4 + 2z + 4z

Combine like terms: -4 + -4 = -8
23 + 7z = -8 + 2z + 4z

Combine like terms: 2z + 4z = 6z
23 + 7z = -8 + 6z

Solving
23 + 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.
23 + 7z + -6z = -8 + 6z + -6z

Combine like terms: 7z + -6z = 1z
23 + 1z = -8 + 6z + -6z

Combine like terms: 6z + -6z = 0
23 + 1z = -8 + 0
23 + 1z = -8

Add '-23' to each side of the equation.
23 + -23 + 1z = -8 + -23

Combine like terms: 23 + -23 = 0
0 + 1z = -8 + -23
1z = -8 + -23

Combine like terms: -8 + -23 = -31
1z = -31

Divide each side by '1'.
z = -31

Simplifying
z = -31