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

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Solution for 12(z+3)-4(z-1)=4(z-1)+3(z-3) equation: 


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

Reorder the terms:
12(3 + z) + -4(z + -1) = 4(z + -1) + 3(z + -3)
(3 * 12 + z * 12) + -4(z + -1) = 4(z + -1) + 3(z + -3)
(36 + 12z) + -4(z + -1) = 4(z + -1) + 3(z + -3)

Reorder the terms:
36 + 12z + -4(-1 + z) = 4(z + -1) + 3(z + -3)
36 + 12z + (-1 * -4 + z * -4) = 4(z + -1) + 3(z + -3)
36 + 12z + (4 + -4z) = 4(z + -1) + 3(z + -3)

Reorder the terms:
36 + 4 + 12z + -4z = 4(z + -1) + 3(z + -3)

Combine like terms: 36 + 4 = 40
40 + 12z + -4z = 4(z + -1) + 3(z + -3)

Combine like terms: 12z + -4z = 8z
40 + 8z = 4(z + -1) + 3(z + -3)

Reorder the terms:
40 + 8z = 4(-1 + z) + 3(z + -3)
40 + 8z = (-1 * 4 + z * 4) + 3(z + -3)
40 + 8z = (-4 + 4z) + 3(z + -3)

Reorder the terms:
40 + 8z = -4 + 4z + 3(-3 + z)
40 + 8z = -4 + 4z + (-3 * 3 + z * 3)
40 + 8z = -4 + 4z + (-9 + 3z)

Reorder the terms:
40 + 8z = -4 + -9 + 4z + 3z

Combine like terms: -4 + -9 = -13
40 + 8z = -13 + 4z + 3z

Combine like terms: 4z + 3z = 7z
40 + 8z = -13 + 7z

Solving
40 + 8z = -13 + 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.
40 + 8z + -7z = -13 + 7z + -7z

Combine like terms: 8z + -7z = 1z
40 + 1z = -13 + 7z + -7z

Combine like terms: 7z + -7z = 0
40 + 1z = -13 + 0
40 + 1z = -13

Add '-40' to each side of the equation.
40 + -40 + 1z = -13 + -40

Combine like terms: 40 + -40 = 0
0 + 1z = -13 + -40
1z = -13 + -40

Combine like terms: -13 + -40 = -53
1z = -53

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

Simplifying
z = -53

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