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

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

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

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

Reorder the terms:
30 + 10z + -3(-3 + z) = 4(z + -4) + 2(z + -3)
30 + 10z + (-3 * -3 + z * -3) = 4(z + -4) + 2(z + -3)
30 + 10z + (9 + -3z) = 4(z + -4) + 2(z + -3)

Reorder the terms:
30 + 9 + 10z + -3z = 4(z + -4) + 2(z + -3)

Combine like terms: 30 + 9 = 39
39 + 10z + -3z = 4(z + -4) + 2(z + -3)

Combine like terms: 10z + -3z = 7z
39 + 7z = 4(z + -4) + 2(z + -3)

Reorder the terms:
39 + 7z = 4(-4 + z) + 2(z + -3)
39 + 7z = (-4 * 4 + z * 4) + 2(z + -3)
39 + 7z = (-16 + 4z) + 2(z + -3)

Reorder the terms:
39 + 7z = -16 + 4z + 2(-3 + z)
39 + 7z = -16 + 4z + (-3 * 2 + z * 2)
39 + 7z = -16 + 4z + (-6 + 2z)

Reorder the terms:
39 + 7z = -16 + -6 + 4z + 2z

Combine like terms: -16 + -6 = -22
39 + 7z = -22 + 4z + 2z

Combine like terms: 4z + 2z = 6z
39 + 7z = -22 + 6z

Solving
39 + 7z = -22 + 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.
39 + 7z + -6z = -22 + 6z + -6z

Combine like terms: 7z + -6z = 1z
39 + 1z = -22 + 6z + -6z

Combine like terms: 6z + -6z = 0
39 + 1z = -22 + 0
39 + 1z = -22

Add '-39' to each side of the equation.
39 + -39 + 1z = -22 + -39

Combine like terms: 39 + -39 = 0
0 + 1z = -22 + -39
1z = -22 + -39

Combine like terms: -22 + -39 = -61
1z = -61

Divide each side by '1'.
z = -61

Simplifying
z = -61