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

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Solution for 12(z+2)-4(z-4)=3(z-2)+4(z-1) equation: 


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

Reorder the terms:
12(2 + z) + -4(z + -4) = 3(z + -2) + 4(z + -1)
(2 * 12 + z * 12) + -4(z + -4) = 3(z + -2) + 4(z + -1)
(24 + 12z) + -4(z + -4) = 3(z + -2) + 4(z + -1)

Reorder the terms:
24 + 12z + -4(-4 + z) = 3(z + -2) + 4(z + -1)
24 + 12z + (-4 * -4 + z * -4) = 3(z + -2) + 4(z + -1)
24 + 12z + (16 + -4z) = 3(z + -2) + 4(z + -1)

Reorder the terms:
24 + 16 + 12z + -4z = 3(z + -2) + 4(z + -1)

Combine like terms: 24 + 16 = 40
40 + 12z + -4z = 3(z + -2) + 4(z + -1)

Combine like terms: 12z + -4z = 8z
40 + 8z = 3(z + -2) + 4(z + -1)

Reorder the terms:
40 + 8z = 3(-2 + z) + 4(z + -1)
40 + 8z = (-2 * 3 + z * 3) + 4(z + -1)
40 + 8z = (-6 + 3z) + 4(z + -1)

Reorder the terms:
40 + 8z = -6 + 3z + 4(-1 + z)
40 + 8z = -6 + 3z + (-1 * 4 + z * 4)
40 + 8z = -6 + 3z + (-4 + 4z)

Reorder the terms:
40 + 8z = -6 + -4 + 3z + 4z

Combine like terms: -6 + -4 = -10
40 + 8z = -10 + 3z + 4z

Combine like terms: 3z + 4z = 7z
40 + 8z = -10 + 7z

Solving
40 + 8z = -10 + 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 = -10 + 7z + -7z

Combine like terms: 8z + -7z = 1z
40 + 1z = -10 + 7z + -7z

Combine like terms: 7z + -7z = 0
40 + 1z = -10 + 0
40 + 1z = -10

Add '-40' to each side of the equation.
40 + -40 + 1z = -10 + -40

Combine like terms: 40 + -40 = 0
0 + 1z = -10 + -40
1z = -10 + -40

Combine like terms: -10 + -40 = -50
1z = -50

Divide each side by '1'.
z = -50

Simplifying
z = -50

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