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

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

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

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

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

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

Combine like terms: 30 + 4 = 34
34 + 10z + -4z = 3(z + -2) + 2(z + -2)

Combine like terms: 10z + -4z = 6z
34 + 6z = 3(z + -2) + 2(z + -2)

Reorder the terms:
34 + 6z = 3(-2 + z) + 2(z + -2)
34 + 6z = (-2 * 3 + z * 3) + 2(z + -2)
34 + 6z = (-6 + 3z) + 2(z + -2)

Reorder the terms:
34 + 6z = -6 + 3z + 2(-2 + z)
34 + 6z = -6 + 3z + (-2 * 2 + z * 2)
34 + 6z = -6 + 3z + (-4 + 2z)

Reorder the terms:
34 + 6z = -6 + -4 + 3z + 2z

Combine like terms: -6 + -4 = -10
34 + 6z = -10 + 3z + 2z

Combine like terms: 3z + 2z = 5z
34 + 6z = -10 + 5z

Solving
34 + 6z = -10 + 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.
34 + 6z + -5z = -10 + 5z + -5z

Combine like terms: 6z + -5z = 1z
34 + 1z = -10 + 5z + -5z

Combine like terms: 5z + -5z = 0
34 + 1z = -10 + 0
34 + 1z = -10

Add '-34' to each side of the equation.
34 + -34 + 1z = -10 + -34

Combine like terms: 34 + -34 = 0
0 + 1z = -10 + -34
1z = -10 + -34

Combine like terms: -10 + -34 = -44
1z = -44

Divide each side by '1'.
z = -44

Simplifying
z = -44