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

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

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

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

Reorder the terms:
10 + 10z + -3(-2 + z) = 2(z + -1) + 4(z + -3)
10 + 10z + (-2 * -3 + z * -3) = 2(z + -1) + 4(z + -3)
10 + 10z + (6 + -3z) = 2(z + -1) + 4(z + -3)

Reorder the terms:
10 + 6 + 10z + -3z = 2(z + -1) + 4(z + -3)

Combine like terms: 10 + 6 = 16
16 + 10z + -3z = 2(z + -1) + 4(z + -3)

Combine like terms: 10z + -3z = 7z
16 + 7z = 2(z + -1) + 4(z + -3)

Reorder the terms:
16 + 7z = 2(-1 + z) + 4(z + -3)
16 + 7z = (-1 * 2 + z * 2) + 4(z + -3)
16 + 7z = (-2 + 2z) + 4(z + -3)

Reorder the terms:
16 + 7z = -2 + 2z + 4(-3 + z)
16 + 7z = -2 + 2z + (-3 * 4 + z * 4)
16 + 7z = -2 + 2z + (-12 + 4z)

Reorder the terms:
16 + 7z = -2 + -12 + 2z + 4z

Combine like terms: -2 + -12 = -14
16 + 7z = -14 + 2z + 4z

Combine like terms: 2z + 4z = 6z
16 + 7z = -14 + 6z

Solving
16 + 7z = -14 + 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.
16 + 7z + -6z = -14 + 6z + -6z

Combine like terms: 7z + -6z = 1z
16 + 1z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
16 + 1z = -14 + 0
16 + 1z = -14

Add '-16' to each side of the equation.
16 + -16 + 1z = -14 + -16

Combine like terms: 16 + -16 = 0
0 + 1z = -14 + -16
1z = -14 + -16

Combine like terms: -14 + -16 = -30
1z = -30

Divide each side by '1'.
z = -30

Simplifying
z = -30