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

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


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

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

Reorder the terms:
52 + 13z + -4(-4 + z) = 4(z + -4) + 4(z + -2)
52 + 13z + (-4 * -4 + z * -4) = 4(z + -4) + 4(z + -2)
52 + 13z + (16 + -4z) = 4(z + -4) + 4(z + -2)

Reorder the terms:
52 + 16 + 13z + -4z = 4(z + -4) + 4(z + -2)

Combine like terms: 52 + 16 = 68
68 + 13z + -4z = 4(z + -4) + 4(z + -2)

Combine like terms: 13z + -4z = 9z
68 + 9z = 4(z + -4) + 4(z + -2)

Reorder the terms:
68 + 9z = 4(-4 + z) + 4(z + -2)
68 + 9z = (-4 * 4 + z * 4) + 4(z + -2)
68 + 9z = (-16 + 4z) + 4(z + -2)

Reorder the terms:
68 + 9z = -16 + 4z + 4(-2 + z)
68 + 9z = -16 + 4z + (-2 * 4 + z * 4)
68 + 9z = -16 + 4z + (-8 + 4z)

Reorder the terms:
68 + 9z = -16 + -8 + 4z + 4z

Combine like terms: -16 + -8 = -24
68 + 9z = -24 + 4z + 4z

Combine like terms: 4z + 4z = 8z
68 + 9z = -24 + 8z

Solving
68 + 9z = -24 + 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.
68 + 9z + -8z = -24 + 8z + -8z

Combine like terms: 9z + -8z = 1z
68 + 1z = -24 + 8z + -8z

Combine like terms: 8z + -8z = 0
68 + 1z = -24 + 0
68 + 1z = -24

Add '-68' to each side of the equation.
68 + -68 + 1z = -24 + -68

Combine like terms: 68 + -68 = 0
0 + 1z = -24 + -68
1z = -24 + -68

Combine like terms: -24 + -68 = -92
1z = -92

Divide each side by '1'.
z = -92

Simplifying
z = -92

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