(6r-3)+(8z-5)=(12z-4)-2(1+z)

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Solution for (6r-3)+(8z-5)=(12z-4)-2(1+z) equation: 


Simplifying
(6r + -3) + (8z + -5) = (12z + -4) + -2(1 + z)

Reorder the terms:
(-3 + 6r) + (8z + -5) = (12z + -4) + -2(1 + z)

Remove parenthesis around (-3 + 6r)
-3 + 6r + (8z + -5) = (12z + -4) + -2(1 + z)

Reorder the terms:
-3 + 6r + (-5 + 8z) = (12z + -4) + -2(1 + z)

Remove parenthesis around (-5 + 8z)
-3 + 6r + -5 + 8z = (12z + -4) + -2(1 + z)

Reorder the terms:
-3 + -5 + 6r + 8z = (12z + -4) + -2(1 + z)

Combine like terms: -3 + -5 = -8
-8 + 6r + 8z = (12z + -4) + -2(1 + z)

Reorder the terms:
-8 + 6r + 8z = (-4 + 12z) + -2(1 + z)

Remove parenthesis around (-4 + 12z)
-8 + 6r + 8z = -4 + 12z + -2(1 + z)
-8 + 6r + 8z = -4 + 12z + (1 * -2 + z * -2)
-8 + 6r + 8z = -4 + 12z + (-2 + -2z)

Reorder the terms:
-8 + 6r + 8z = -4 + -2 + 12z + -2z

Combine like terms: -4 + -2 = -6
-8 + 6r + 8z = -6 + 12z + -2z

Combine like terms: 12z + -2z = 10z
-8 + 6r + 8z = -6 + 10z

Solving
-8 + 6r + 8z = -6 + 10z

Solving for variable 'r'.

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

Add '8' to each side of the equation.
-8 + 6r + 8 + 8z = -6 + 8 + 10z

Reorder the terms:
-8 + 8 + 6r + 8z = -6 + 8 + 10z

Combine like terms: -8 + 8 = 0
0 + 6r + 8z = -6 + 8 + 10z
6r + 8z = -6 + 8 + 10z

Combine like terms: -6 + 8 = 2
6r + 8z = 2 + 10z

Add '-8z' to each side of the equation.
6r + 8z + -8z = 2 + 10z + -8z

Combine like terms: 8z + -8z = 0
6r + 0 = 2 + 10z + -8z
6r = 2 + 10z + -8z

Combine like terms: 10z + -8z = 2z
6r = 2 + 2z

Divide each side by '6'.
r = 0.3333333333 + 0.3333333333z

Simplifying
r = 0.3333333333 + 0.3333333333z

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