.4(2z+6)+.1=.5(2z-3)

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


Simplifying
0.4(2z + 6) + 0.1 = 0.5(2z + -3)

Reorder the terms:
0.4(6 + 2z) + 0.1 = 0.5(2z + -3)
(6 * 0.4 + 2z * 0.4) + 0.1 = 0.5(2z + -3)
(2.4 + 0.8z) + 0.1 = 0.5(2z + -3)

Reorder the terms:
2.4 + 0.1 + 0.8z = 0.5(2z + -3)

Combine like terms: 2.4 + 0.1 = 2.5
2.5 + 0.8z = 0.5(2z + -3)

Reorder the terms:
2.5 + 0.8z = 0.5(-3 + 2z)
2.5 + 0.8z = (-3 * 0.5 + 2z * 0.5)
2.5 + 0.8z = (-1.5 + 1z)

Solving
2.5 + 0.8z = -1.5 + 1z

Solving for variable 'z'.

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

Add '-1z' to each side of the equation.
2.5 + 0.8z + -1z = -1.5 + 1z + -1z

Combine like terms: 0.8z + -1z = -0.2z
2.5 + -0.2z = -1.5 + 1z + -1z

Combine like terms: 1z + -1z = 0
2.5 + -0.2z = -1.5 + 0
2.5 + -0.2z = -1.5

Add '-2.5' to each side of the equation.
2.5 + -2.5 + -0.2z = -1.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.2z = -1.5 + -2.5
-0.2z = -1.5 + -2.5

Combine like terms: -1.5 + -2.5 = -4
-0.2z = -4

Divide each side by '-0.2'.
z = 20

Simplifying
z = 20

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