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

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

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

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

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

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

Combine like terms: 10 + 12 = 22
22 + 10z + -3z = 4(z + -3) + 2(z + -1)

Combine like terms: 10z + -3z = 7z
22 + 7z = 4(z + -3) + 2(z + -1)

Reorder the terms:
22 + 7z = 4(-3 + z) + 2(z + -1)
22 + 7z = (-3 * 4 + z * 4) + 2(z + -1)
22 + 7z = (-12 + 4z) + 2(z + -1)

Reorder the terms:
22 + 7z = -12 + 4z + 2(-1 + z)
22 + 7z = -12 + 4z + (-1 * 2 + z * 2)
22 + 7z = -12 + 4z + (-2 + 2z)

Reorder the terms:
22 + 7z = -12 + -2 + 4z + 2z

Combine like terms: -12 + -2 = -14
22 + 7z = -14 + 4z + 2z

Combine like terms: 4z + 2z = 6z
22 + 7z = -14 + 6z

Solving
22 + 7z = -14 + 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.
22 + 7z + -6z = -14 + 6z + -6z

Combine like terms: 7z + -6z = 1z
22 + 1z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
22 + 1z = -14 + 0
22 + 1z = -14

Add '-22' to each side of the equation.
22 + -22 + 1z = -14 + -22

Combine like terms: 22 + -22 = 0
0 + 1z = -14 + -22
1z = -14 + -22

Combine like terms: -14 + -22 = -36
1z = -36

Divide each side by '1'.
z = -36

Simplifying
z = -36