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

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

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

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

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

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

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

Combine like terms: 10z + -4z = 6z
22 + 6z = 3(z + -1) + 2(z + -4)

Reorder the terms:
22 + 6z = 3(-1 + z) + 2(z + -4)
22 + 6z = (-1 * 3 + z * 3) + 2(z + -4)
22 + 6z = (-3 + 3z) + 2(z + -4)

Reorder the terms:
22 + 6z = -3 + 3z + 2(-4 + z)
22 + 6z = -3 + 3z + (-4 * 2 + z * 2)
22 + 6z = -3 + 3z + (-8 + 2z)

Reorder the terms:
22 + 6z = -3 + -8 + 3z + 2z

Combine like terms: -3 + -8 = -11
22 + 6z = -11 + 3z + 2z

Combine like terms: 3z + 2z = 5z
22 + 6z = -11 + 5z

Solving
22 + 6z = -11 + 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.
22 + 6z + -5z = -11 + 5z + -5z

Combine like terms: 6z + -5z = 1z
22 + 1z = -11 + 5z + -5z

Combine like terms: 5z + -5z = 0
22 + 1z = -11 + 0
22 + 1z = -11

Add '-22' to each side of the equation.
22 + -22 + 1z = -11 + -22

Combine like terms: 22 + -22 = 0
0 + 1z = -11 + -22
1z = -11 + -22

Combine like terms: -11 + -22 = -33
1z = -33

Divide each side by '1'.
z = -33

Simplifying
z = -33