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

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

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

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

Reorder the terms:
20 + 10z + -2(-4 + z) = 3(z + -4) + 4(z + -3)
20 + 10z + (-4 * -2 + z * -2) = 3(z + -4) + 4(z + -3)
20 + 10z + (8 + -2z) = 3(z + -4) + 4(z + -3)

Reorder the terms:
20 + 8 + 10z + -2z = 3(z + -4) + 4(z + -3)

Combine like terms: 20 + 8 = 28
28 + 10z + -2z = 3(z + -4) + 4(z + -3)

Combine like terms: 10z + -2z = 8z
28 + 8z = 3(z + -4) + 4(z + -3)

Reorder the terms:
28 + 8z = 3(-4 + z) + 4(z + -3)
28 + 8z = (-4 * 3 + z * 3) + 4(z + -3)
28 + 8z = (-12 + 3z) + 4(z + -3)

Reorder the terms:
28 + 8z = -12 + 3z + 4(-3 + z)
28 + 8z = -12 + 3z + (-3 * 4 + z * 4)
28 + 8z = -12 + 3z + (-12 + 4z)

Reorder the terms:
28 + 8z = -12 + -12 + 3z + 4z

Combine like terms: -12 + -12 = -24
28 + 8z = -24 + 3z + 4z

Combine like terms: 3z + 4z = 7z
28 + 8z = -24 + 7z

Solving
28 + 8z = -24 + 7z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-7z' to each side of the equation.
28 + 8z + -7z = -24 + 7z + -7z

Combine like terms: 8z + -7z = 1z
28 + 1z = -24 + 7z + -7z

Combine like terms: 7z + -7z = 0
28 + 1z = -24 + 0
28 + 1z = -24

Add '-28' to each side of the equation.
28 + -28 + 1z = -24 + -28

Combine like terms: 28 + -28 = 0
0 + 1z = -24 + -28
1z = -24 + -28

Combine like terms: -24 + -28 = -52
1z = -52

Divide each side by '1'.
z = -52

Simplifying
z = -52