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

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


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

Reorder the terms:
13(3 + z) + -4(z + -3) = 4(z + -2) + 4(z + -1)
(3 * 13 + z * 13) + -4(z + -3) = 4(z + -2) + 4(z + -1)
(39 + 13z) + -4(z + -3) = 4(z + -2) + 4(z + -1)

Reorder the terms:
39 + 13z + -4(-3 + z) = 4(z + -2) + 4(z + -1)
39 + 13z + (-3 * -4 + z * -4) = 4(z + -2) + 4(z + -1)
39 + 13z + (12 + -4z) = 4(z + -2) + 4(z + -1)

Reorder the terms:
39 + 12 + 13z + -4z = 4(z + -2) + 4(z + -1)

Combine like terms: 39 + 12 = 51
51 + 13z + -4z = 4(z + -2) + 4(z + -1)

Combine like terms: 13z + -4z = 9z
51 + 9z = 4(z + -2) + 4(z + -1)

Reorder the terms:
51 + 9z = 4(-2 + z) + 4(z + -1)
51 + 9z = (-2 * 4 + z * 4) + 4(z + -1)
51 + 9z = (-8 + 4z) + 4(z + -1)

Reorder the terms:
51 + 9z = -8 + 4z + 4(-1 + z)
51 + 9z = -8 + 4z + (-1 * 4 + z * 4)
51 + 9z = -8 + 4z + (-4 + 4z)

Reorder the terms:
51 + 9z = -8 + -4 + 4z + 4z

Combine like terms: -8 + -4 = -12
51 + 9z = -12 + 4z + 4z

Combine like terms: 4z + 4z = 8z
51 + 9z = -12 + 8z

Solving
51 + 9z = -12 + 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.
51 + 9z + -8z = -12 + 8z + -8z

Combine like terms: 9z + -8z = 1z
51 + 1z = -12 + 8z + -8z

Combine like terms: 8z + -8z = 0
51 + 1z = -12 + 0
51 + 1z = -12

Add '-51' to each side of the equation.
51 + -51 + 1z = -12 + -51

Combine like terms: 51 + -51 = 0
0 + 1z = -12 + -51
1z = -12 + -51

Combine like terms: -12 + -51 = -63
1z = -63

Divide each side by '1'.
z = -63

Simplifying
z = -63

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