11(z+1)-4(z-4)=4(z-4)+2(z-4)

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Solution for 11(z+1)-4(z-4)=4(z-4)+2(z-4) equation: 


Simplifying
11(z + 1) + -4(z + -4) = 4(z + -4) + 2(z + -4)

Reorder the terms:
11(1 + z) + -4(z + -4) = 4(z + -4) + 2(z + -4)
(1 * 11 + z * 11) + -4(z + -4) = 4(z + -4) + 2(z + -4)
(11 + 11z) + -4(z + -4) = 4(z + -4) + 2(z + -4)

Reorder the terms:
11 + 11z + -4(-4 + z) = 4(z + -4) + 2(z + -4)
11 + 11z + (-4 * -4 + z * -4) = 4(z + -4) + 2(z + -4)
11 + 11z + (16 + -4z) = 4(z + -4) + 2(z + -4)

Reorder the terms:
11 + 16 + 11z + -4z = 4(z + -4) + 2(z + -4)

Combine like terms: 11 + 16 = 27
27 + 11z + -4z = 4(z + -4) + 2(z + -4)

Combine like terms: 11z + -4z = 7z
27 + 7z = 4(z + -4) + 2(z + -4)

Reorder the terms:
27 + 7z = 4(-4 + z) + 2(z + -4)
27 + 7z = (-4 * 4 + z * 4) + 2(z + -4)
27 + 7z = (-16 + 4z) + 2(z + -4)

Reorder the terms:
27 + 7z = -16 + 4z + 2(-4 + z)
27 + 7z = -16 + 4z + (-4 * 2 + z * 2)
27 + 7z = -16 + 4z + (-8 + 2z)

Reorder the terms:
27 + 7z = -16 + -8 + 4z + 2z

Combine like terms: -16 + -8 = -24
27 + 7z = -24 + 4z + 2z

Combine like terms: 4z + 2z = 6z
27 + 7z = -24 + 6z

Solving
27 + 7z = -24 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
27 + 7z + -6z = -24 + 6z + -6z

Combine like terms: 7z + -6z = 1z
27 + 1z = -24 + 6z + -6z

Combine like terms: 6z + -6z = 0
27 + 1z = -24 + 0
27 + 1z = -24

Add '-27' to each side of the equation.
27 + -27 + 1z = -24 + -27

Combine like terms: 27 + -27 = 0
0 + 1z = -24 + -27
1z = -24 + -27

Combine like terms: -24 + -27 = -51
1z = -51

Divide each side by '1'.
z = -51

Simplifying
z = -51

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