0.4(4z+5)+7.5=.5(4z-5)

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Solution for 0.4(4z+5)+7.5=.5(4z-5) equation: 


Simplifying
0.4(4z + 5) + 7.5 = 0.5(4z + -5)

Reorder the terms:
0.4(5 + 4z) + 7.5 = 0.5(4z + -5)
(5 * 0.4 + 4z * 0.4) + 7.5 = 0.5(4z + -5)
(2 + 1.6z) + 7.5 = 0.5(4z + -5)

Reorder the terms:
2 + 7.5 + 1.6z = 0.5(4z + -5)

Combine like terms: 2 + 7.5 = 9.5
9.5 + 1.6z = 0.5(4z + -5)

Reorder the terms:
9.5 + 1.6z = 0.5(-5 + 4z)
9.5 + 1.6z = (-5 * 0.5 + 4z * 0.5)
9.5 + 1.6z = (-2.5 + 2z)

Solving
9.5 + 1.6z = -2.5 + 2z

Solving for variable 'z'.

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

Add '-2z' to each side of the equation.
9.5 + 1.6z + -2z = -2.5 + 2z + -2z

Combine like terms: 1.6z + -2z = -0.4z
9.5 + -0.4z = -2.5 + 2z + -2z

Combine like terms: 2z + -2z = 0
9.5 + -0.4z = -2.5 + 0
9.5 + -0.4z = -2.5

Add '-9.5' to each side of the equation.
9.5 + -9.5 + -0.4z = -2.5 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + -0.4z = -2.5 + -9.5
-0.4z = -2.5 + -9.5

Combine like terms: -2.5 + -9.5 = -12
-0.4z = -12

Divide each side by '-0.4'.
z = 30

Simplifying
z = 30

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