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

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


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

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

Reorder the terms:
12 + 12z + -4(-4 + z) = 4(z + -3) + 3(z + -1)
12 + 12z + (-4 * -4 + z * -4) = 4(z + -3) + 3(z + -1)
12 + 12z + (16 + -4z) = 4(z + -3) + 3(z + -1)

Reorder the terms:
12 + 16 + 12z + -4z = 4(z + -3) + 3(z + -1)

Combine like terms: 12 + 16 = 28
28 + 12z + -4z = 4(z + -3) + 3(z + -1)

Combine like terms: 12z + -4z = 8z
28 + 8z = 4(z + -3) + 3(z + -1)

Reorder the terms:
28 + 8z = 4(-3 + z) + 3(z + -1)
28 + 8z = (-3 * 4 + z * 4) + 3(z + -1)
28 + 8z = (-12 + 4z) + 3(z + -1)

Reorder the terms:
28 + 8z = -12 + 4z + 3(-1 + z)
28 + 8z = -12 + 4z + (-1 * 3 + z * 3)
28 + 8z = -12 + 4z + (-3 + 3z)

Reorder the terms:
28 + 8z = -12 + -3 + 4z + 3z

Combine like terms: -12 + -3 = -15
28 + 8z = -15 + 4z + 3z

Combine like terms: 4z + 3z = 7z
28 + 8z = -15 + 7z

Solving
28 + 8z = -15 + 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.
28 + 8z + -7z = -15 + 7z + -7z

Combine like terms: 8z + -7z = 1z
28 + 1z = -15 + 7z + -7z

Combine like terms: 7z + -7z = 0
28 + 1z = -15 + 0
28 + 1z = -15

Add '-28' to each side of the equation.
28 + -28 + 1z = -15 + -28

Combine like terms: 28 + -28 = 0
0 + 1z = -15 + -28
1z = -15 + -28

Combine like terms: -15 + -28 = -43
1z = -43

Divide each side by '1'.
z = -43

Simplifying
z = -43

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