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

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


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

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

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

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

Combine like terms: 12 + 12 = 24
24 + 12z + -4z = 4(z + -4) + 3(z + -3)

Combine like terms: 12z + -4z = 8z
24 + 8z = 4(z + -4) + 3(z + -3)

Reorder the terms:
24 + 8z = 4(-4 + z) + 3(z + -3)
24 + 8z = (-4 * 4 + z * 4) + 3(z + -3)
24 + 8z = (-16 + 4z) + 3(z + -3)

Reorder the terms:
24 + 8z = -16 + 4z + 3(-3 + z)
24 + 8z = -16 + 4z + (-3 * 3 + z * 3)
24 + 8z = -16 + 4z + (-9 + 3z)

Reorder the terms:
24 + 8z = -16 + -9 + 4z + 3z

Combine like terms: -16 + -9 = -25
24 + 8z = -25 + 4z + 3z

Combine like terms: 4z + 3z = 7z
24 + 8z = -25 + 7z

Solving
24 + 8z = -25 + 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.
24 + 8z + -7z = -25 + 7z + -7z

Combine like terms: 8z + -7z = 1z
24 + 1z = -25 + 7z + -7z

Combine like terms: 7z + -7z = 0
24 + 1z = -25 + 0
24 + 1z = -25

Add '-24' to each side of the equation.
24 + -24 + 1z = -25 + -24

Combine like terms: 24 + -24 = 0
0 + 1z = -25 + -24
1z = -25 + -24

Combine like terms: -25 + -24 = -49
1z = -49

Divide each side by '1'.
z = -49

Simplifying
z = -49

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