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

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

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

Reorder the terms:
10(3 + z) + -2(z + -1) = 3(z + -1) + 4(z + -4)
(3 * 10 + z * 10) + -2(z + -1) = 3(z + -1) + 4(z + -4)
(30 + 10z) + -2(z + -1) = 3(z + -1) + 4(z + -4)

Reorder the terms:
30 + 10z + -2(-1 + z) = 3(z + -1) + 4(z + -4)
30 + 10z + (-1 * -2 + z * -2) = 3(z + -1) + 4(z + -4)
30 + 10z + (2 + -2z) = 3(z + -1) + 4(z + -4)

Reorder the terms:
30 + 2 + 10z + -2z = 3(z + -1) + 4(z + -4)

Combine like terms: 30 + 2 = 32
32 + 10z + -2z = 3(z + -1) + 4(z + -4)

Combine like terms: 10z + -2z = 8z
32 + 8z = 3(z + -1) + 4(z + -4)

Reorder the terms:
32 + 8z = 3(-1 + z) + 4(z + -4)
32 + 8z = (-1 * 3 + z * 3) + 4(z + -4)
32 + 8z = (-3 + 3z) + 4(z + -4)

Reorder the terms:
32 + 8z = -3 + 3z + 4(-4 + z)
32 + 8z = -3 + 3z + (-4 * 4 + z * 4)
32 + 8z = -3 + 3z + (-16 + 4z)

Reorder the terms:
32 + 8z = -3 + -16 + 3z + 4z

Combine like terms: -3 + -16 = -19
32 + 8z = -19 + 3z + 4z

Combine like terms: 3z + 4z = 7z
32 + 8z = -19 + 7z

Solving
32 + 8z = -19 + 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.
32 + 8z + -7z = -19 + 7z + -7z

Combine like terms: 8z + -7z = 1z
32 + 1z = -19 + 7z + -7z

Combine like terms: 7z + -7z = 0
32 + 1z = -19 + 0
32 + 1z = -19

Add '-32' to each side of the equation.
32 + -32 + 1z = -19 + -32

Combine like terms: 32 + -32 = 0
0 + 1z = -19 + -32
1z = -19 + -32

Combine like terms: -19 + -32 = -51
1z = -51

Divide each side by '1'.
z = -51

Simplifying
z = -51