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

Solution for 13(z+4)-4(z-1)=4(z-2)+4(z-3) equation:

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

Reorder the terms:
13(4 + z) + -4(z + -1) = 4(z + -2) + 4(z + -3)
(4 * 13 + z * 13) + -4(z + -1) = 4(z + -2) + 4(z + -3)
(52 + 13z) + -4(z + -1) = 4(z + -2) + 4(z + -3)

Reorder the terms:
52 + 13z + -4(-1 + z) = 4(z + -2) + 4(z + -3)
52 + 13z + (-1 * -4 + z * -4) = 4(z + -2) + 4(z + -3)
52 + 13z + (4 + -4z) = 4(z + -2) + 4(z + -3)

Reorder the terms:
52 + 4 + 13z + -4z = 4(z + -2) + 4(z + -3)

Combine like terms: 52 + 4 = 56
56 + 13z + -4z = 4(z + -2) + 4(z + -3)

Combine like terms: 13z + -4z = 9z
56 + 9z = 4(z + -2) + 4(z + -3)

Reorder the terms:
56 + 9z = 4(-2 + z) + 4(z + -3)
56 + 9z = (-2 * 4 + z * 4) + 4(z + -3)
56 + 9z = (-8 + 4z) + 4(z + -3)

Reorder the terms:
56 + 9z = -8 + 4z + 4(-3 + z)
56 + 9z = -8 + 4z + (-3 * 4 + z * 4)
56 + 9z = -8 + 4z + (-12 + 4z)

Reorder the terms:
56 + 9z = -8 + -12 + 4z + 4z

Combine like terms: -8 + -12 = -20
56 + 9z = -20 + 4z + 4z

Combine like terms: 4z + 4z = 8z
56 + 9z = -20 + 8z

Solving
56 + 9z = -20 + 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.
56 + 9z + -8z = -20 + 8z + -8z

Combine like terms: 9z + -8z = 1z
56 + 1z = -20 + 8z + -8z

Combine like terms: 8z + -8z = 0
56 + 1z = -20 + 0
56 + 1z = -20

Add '-56' to each side of the equation.
56 + -56 + 1z = -20 + -56

Combine like terms: 56 + -56 = 0
0 + 1z = -20 + -56
1z = -20 + -56

Combine like terms: -20 + -56 = -76
1z = -76

Divide each side by '1'.
z = -76

Simplifying
z = -76