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

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

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

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

Reorder the terms:
10 + 10z + -3(-3 + z) = 4(z + -2) + (z + -1)
10 + 10z + (-3 * -3 + z * -3) = 4(z + -2) + (z + -1)
10 + 10z + (9 + -3z) = 4(z + -2) + (z + -1)

Reorder the terms:
10 + 9 + 10z + -3z = 4(z + -2) + (z + -1)

Combine like terms: 10 + 9 = 19
19 + 10z + -3z = 4(z + -2) + (z + -1)

Combine like terms: 10z + -3z = 7z
19 + 7z = 4(z + -2) + (z + -1)

Reorder the terms:
19 + 7z = 4(-2 + z) + (z + -1)
19 + 7z = (-2 * 4 + z * 4) + (z + -1)
19 + 7z = (-8 + 4z) + (z + -1)

Reorder the terms:
19 + 7z = -8 + 4z + (-1 + z)

Remove parenthesis around (-1 + z)
19 + 7z = -8 + 4z + -1 + z

Reorder the terms:
19 + 7z = -8 + -1 + 4z + z

Combine like terms: -8 + -1 = -9
19 + 7z = -9 + 4z + z

Combine like terms: 4z + z = 5z
19 + 7z = -9 + 5z

Solving
19 + 7z = -9 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
19 + 7z + -5z = -9 + 5z + -5z

Combine like terms: 7z + -5z = 2z
19 + 2z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
19 + 2z = -9 + 0
19 + 2z = -9

Add '-19' to each side of the equation.
19 + -19 + 2z = -9 + -19

Combine like terms: 19 + -19 = 0
0 + 2z = -9 + -19
2z = -9 + -19

Combine like terms: -9 + -19 = -28
2z = -28

Divide each side by '2'.
z = -14

Simplifying
z = -14