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

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

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

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

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

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

Combine like terms: 10 + 9 = 19
19 + 10z + -3z = 4(z + -2) + 2(z + -4)

Combine like terms: 10z + -3z = 7z
19 + 7z = 4(z + -2) + 2(z + -4)

Reorder the terms:
19 + 7z = 4(-2 + z) + 2(z + -4)
19 + 7z = (-2 * 4 + z * 4) + 2(z + -4)
19 + 7z = (-8 + 4z) + 2(z + -4)

Reorder the terms:
19 + 7z = -8 + 4z + 2(-4 + z)
19 + 7z = -8 + 4z + (-4 * 2 + z * 2)
19 + 7z = -8 + 4z + (-8 + 2z)

Reorder the terms:
19 + 7z = -8 + -8 + 4z + 2z

Combine like terms: -8 + -8 = -16
19 + 7z = -16 + 4z + 2z

Combine like terms: 4z + 2z = 6z
19 + 7z = -16 + 6z

Solving
19 + 7z = -16 + 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.
19 + 7z + -6z = -16 + 6z + -6z

Combine like terms: 7z + -6z = 1z
19 + 1z = -16 + 6z + -6z

Combine like terms: 6z + -6z = 0
19 + 1z = -16 + 0
19 + 1z = -16

Add '-19' to each side of the equation.
19 + -19 + 1z = -16 + -19

Combine like terms: 19 + -19 = 0
0 + 1z = -16 + -19
1z = -16 + -19

Combine like terms: -16 + -19 = -35
1z = -35

Divide each side by '1'.
z = -35

Simplifying
z = -35