12(8z+7)-5(16z-3)=18(4z+3)+31

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Solution for 12(8z+7)-5(16z-3)=18(4z+3)+31 equation: 


Simplifying
12(8z + 7) + -5(16z + -3) = 18(4z + 3) + 31

Reorder the terms:
12(7 + 8z) + -5(16z + -3) = 18(4z + 3) + 31
(7 * 12 + 8z * 12) + -5(16z + -3) = 18(4z + 3) + 31
(84 + 96z) + -5(16z + -3) = 18(4z + 3) + 31

Reorder the terms:
84 + 96z + -5(-3 + 16z) = 18(4z + 3) + 31
84 + 96z + (-3 * -5 + 16z * -5) = 18(4z + 3) + 31
84 + 96z + (15 + -80z) = 18(4z + 3) + 31

Reorder the terms:
84 + 15 + 96z + -80z = 18(4z + 3) + 31

Combine like terms: 84 + 15 = 99
99 + 96z + -80z = 18(4z + 3) + 31

Combine like terms: 96z + -80z = 16z
99 + 16z = 18(4z + 3) + 31

Reorder the terms:
99 + 16z = 18(3 + 4z) + 31
99 + 16z = (3 * 18 + 4z * 18) + 31
99 + 16z = (54 + 72z) + 31

Reorder the terms:
99 + 16z = 54 + 31 + 72z

Combine like terms: 54 + 31 = 85
99 + 16z = 85 + 72z

Solving
99 + 16z = 85 + 72z

Solving for variable 'z'.

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

Add '-72z' to each side of the equation.
99 + 16z + -72z = 85 + 72z + -72z

Combine like terms: 16z + -72z = -56z
99 + -56z = 85 + 72z + -72z

Combine like terms: 72z + -72z = 0
99 + -56z = 85 + 0
99 + -56z = 85

Add '-99' to each side of the equation.
99 + -99 + -56z = 85 + -99

Combine like terms: 99 + -99 = 0
0 + -56z = 85 + -99
-56z = 85 + -99

Combine like terms: 85 + -99 = -14
-56z = -14

Divide each side by '-56'.
z = 0.25

Simplifying
z = 0.25

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