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

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

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

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

Reorder the terms:
30 + 10z + -2(-4 + z) = 4(z + -3) + 3(z + -1)
30 + 10z + (-4 * -2 + z * -2) = 4(z + -3) + 3(z + -1)
30 + 10z + (8 + -2z) = 4(z + -3) + 3(z + -1)

Reorder the terms:
30 + 8 + 10z + -2z = 4(z + -3) + 3(z + -1)

Combine like terms: 30 + 8 = 38
38 + 10z + -2z = 4(z + -3) + 3(z + -1)

Combine like terms: 10z + -2z = 8z
38 + 8z = 4(z + -3) + 3(z + -1)

Reorder the terms:
38 + 8z = 4(-3 + z) + 3(z + -1)
38 + 8z = (-3 * 4 + z * 4) + 3(z + -1)
38 + 8z = (-12 + 4z) + 3(z + -1)

Reorder the terms:
38 + 8z = -12 + 4z + 3(-1 + z)
38 + 8z = -12 + 4z + (-1 * 3 + z * 3)
38 + 8z = -12 + 4z + (-3 + 3z)

Reorder the terms:
38 + 8z = -12 + -3 + 4z + 3z

Combine like terms: -12 + -3 = -15
38 + 8z = -15 + 4z + 3z

Combine like terms: 4z + 3z = 7z
38 + 8z = -15 + 7z

Solving
38 + 8z = -15 + 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.
38 + 8z + -7z = -15 + 7z + -7z

Combine like terms: 8z + -7z = 1z
38 + 1z = -15 + 7z + -7z

Combine like terms: 7z + -7z = 0
38 + 1z = -15 + 0
38 + 1z = -15

Add '-38' to each side of the equation.
38 + -38 + 1z = -15 + -38

Combine like terms: 38 + -38 = 0
0 + 1z = -15 + -38
1z = -15 + -38

Combine like terms: -15 + -38 = -53
1z = -53

Divide each side by '1'.
z = -53

Simplifying
z = -53