.4(3z+5)+30.5=.7(3z-5)

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Solution for .4(3z+5)+30.5=.7(3z-5) equation: 


Simplifying
0.4(3z + 5) + 30.5 = 0.7(3z + -5)

Reorder the terms:
0.4(5 + 3z) + 30.5 = 0.7(3z + -5)
(5 * 0.4 + 3z * 0.4) + 30.5 = 0.7(3z + -5)
(2 + 1.2z) + 30.5 = 0.7(3z + -5)

Reorder the terms:
2 + 30.5 + 1.2z = 0.7(3z + -5)

Combine like terms: 2 + 30.5 = 32.5
32.5 + 1.2z = 0.7(3z + -5)

Reorder the terms:
32.5 + 1.2z = 0.7(-5 + 3z)
32.5 + 1.2z = (-5 * 0.7 + 3z * 0.7)
32.5 + 1.2z = (-3.5 + 2.1z)

Solving
32.5 + 1.2z = -3.5 + 2.1z

Solving for variable 'z'.

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

Add '-2.1z' to each side of the equation.
32.5 + 1.2z + -2.1z = -3.5 + 2.1z + -2.1z

Combine like terms: 1.2z + -2.1z = -0.9z
32.5 + -0.9z = -3.5 + 2.1z + -2.1z

Combine like terms: 2.1z + -2.1z = 0.0
32.5 + -0.9z = -3.5 + 0.0
32.5 + -0.9z = -3.5

Add '-32.5' to each side of the equation.
32.5 + -32.5 + -0.9z = -3.5 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + -0.9z = -3.5 + -32.5
-0.9z = -3.5 + -32.5

Combine like terms: -3.5 + -32.5 = -36
-0.9z = -36

Divide each side by '-0.9'.
z = 40

Simplifying
z = 40

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