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

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

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

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

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

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

Combine like terms: 10 + 8 = 18
18 + 10z + -2z = 3(z + -3) + 4(z + -3)

Combine like terms: 10z + -2z = 8z
18 + 8z = 3(z + -3) + 4(z + -3)

Reorder the terms:
18 + 8z = 3(-3 + z) + 4(z + -3)
18 + 8z = (-3 * 3 + z * 3) + 4(z + -3)
18 + 8z = (-9 + 3z) + 4(z + -3)

Reorder the terms:
18 + 8z = -9 + 3z + 4(-3 + z)
18 + 8z = -9 + 3z + (-3 * 4 + z * 4)
18 + 8z = -9 + 3z + (-12 + 4z)

Reorder the terms:
18 + 8z = -9 + -12 + 3z + 4z

Combine like terms: -9 + -12 = -21
18 + 8z = -21 + 3z + 4z

Combine like terms: 3z + 4z = 7z
18 + 8z = -21 + 7z

Solving
18 + 8z = -21 + 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.
18 + 8z + -7z = -21 + 7z + -7z

Combine like terms: 8z + -7z = 1z
18 + 1z = -21 + 7z + -7z

Combine like terms: 7z + -7z = 0
18 + 1z = -21 + 0
18 + 1z = -21

Add '-18' to each side of the equation.
18 + -18 + 1z = -21 + -18

Combine like terms: 18 + -18 = 0
0 + 1z = -21 + -18
1z = -21 + -18

Combine like terms: -21 + -18 = -39
1z = -39

Divide each side by '1'.
z = -39

Simplifying
z = -39