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

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


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

Reorder the terms:
12(4 + z) + -3(z + -1) = 4(z + -1) + -4(z + -4)
(4 * 12 + z * 12) + -3(z + -1) = 4(z + -1) + -4(z + -4)
(48 + 12z) + -3(z + -1) = 4(z + -1) + -4(z + -4)

Reorder the terms:
48 + 12z + -3(-1 + z) = 4(z + -1) + -4(z + -4)
48 + 12z + (-1 * -3 + z * -3) = 4(z + -1) + -4(z + -4)
48 + 12z + (3 + -3z) = 4(z + -1) + -4(z + -4)

Reorder the terms:
48 + 3 + 12z + -3z = 4(z + -1) + -4(z + -4)

Combine like terms: 48 + 3 = 51
51 + 12z + -3z = 4(z + -1) + -4(z + -4)

Combine like terms: 12z + -3z = 9z
51 + 9z = 4(z + -1) + -4(z + -4)

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

Reorder the terms:
51 + 9z = -4 + 4z + -4(-4 + z)
51 + 9z = -4 + 4z + (-4 * -4 + z * -4)
51 + 9z = -4 + 4z + (16 + -4z)

Reorder the terms:
51 + 9z = -4 + 16 + 4z + -4z

Combine like terms: -4 + 16 = 12
51 + 9z = 12 + 4z + -4z

Combine like terms: 4z + -4z = 0
51 + 9z = 12 + 0
51 + 9z = 12

Solving
51 + 9z = 12

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-51' to each side of the equation.
51 + -51 + 9z = 12 + -51

Combine like terms: 51 + -51 = 0
0 + 9z = 12 + -51
9z = 12 + -51

Combine like terms: 12 + -51 = -39
9z = -39

Divide each side by '9'.
z = -4.333333333

Simplifying
z = -4.333333333

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