13(z+3)-4(z-1)=4(z-1)+4(z-3)

Solution for 13(z+3)-4(z-1)=4(z-1)+4(z-3) equation:

Simplifying
13(z + 3) + -4(z + -1) = 4(z + -1) + 4(z + -3)

Reorder the terms:
13(3 + z) + -4(z + -1) = 4(z + -1) + 4(z + -3)
(3 * 13 + z * 13) + -4(z + -1) = 4(z + -1) + 4(z + -3)
(39 + 13z) + -4(z + -1) = 4(z + -1) + 4(z + -3)

Reorder the terms:
39 + 13z + -4(-1 + z) = 4(z + -1) + 4(z + -3)
39 + 13z + (-1 * -4 + z * -4) = 4(z + -1) + 4(z + -3)
39 + 13z + (4 + -4z) = 4(z + -1) + 4(z + -3)

Reorder the terms:
39 + 4 + 13z + -4z = 4(z + -1) + 4(z + -3)

Combine like terms: 39 + 4 = 43
43 + 13z + -4z = 4(z + -1) + 4(z + -3)

Combine like terms: 13z + -4z = 9z
43 + 9z = 4(z + -1) + 4(z + -3)

Reorder the terms:
43 + 9z = 4(-1 + z) + 4(z + -3)
43 + 9z = (-1 * 4 + z * 4) + 4(z + -3)
43 + 9z = (-4 + 4z) + 4(z + -3)

Reorder the terms:
43 + 9z = -4 + 4z + 4(-3 + z)
43 + 9z = -4 + 4z + (-3 * 4 + z * 4)
43 + 9z = -4 + 4z + (-12 + 4z)

Reorder the terms:
43 + 9z = -4 + -12 + 4z + 4z

Combine like terms: -4 + -12 = -16
43 + 9z = -16 + 4z + 4z

Combine like terms: 4z + 4z = 8z
43 + 9z = -16 + 8z

Solving
43 + 9z = -16 + 8z

Solving for variable 'z'.

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

Add '-8z' to each side of the equation.
43 + 9z + -8z = -16 + 8z + -8z

Combine like terms: 9z + -8z = 1z
43 + 1z = -16 + 8z + -8z

Combine like terms: 8z + -8z = 0
43 + 1z = -16 + 0
43 + 1z = -16

Add '-43' to each side of the equation.
43 + -43 + 1z = -16 + -43

Combine like terms: 43 + -43 = 0
0 + 1z = -16 + -43
1z = -16 + -43

Combine like terms: -16 + -43 = -59
1z = -59

Divide each side by '1'.
z = -59

Simplifying
z = -59