SOLUTION: How do I solve for z? 1/3z+15+4=8/z+5

Question 60652: How do I solve for z?
1/3z+15+4=8/z+5

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
How do I solve for z?
1/3z+15+4=8/z+5
:
Assume you mean:

:
Get rid of the denominators, mult eq by (3z+15)(z+5), resulting in:
(z+5) + 4(3z+15)(z+5) = 8(3z+15)
:
(z+5) + 4(3z^2 + 30z + 75) = 24z + 120
:
z + 5 + 12z^2 + 120z + 300 = 24z + 120
:
12z^2 + z + 120z - 24z + 5 + 300 - 120 = 0
:
12z^2 + 97z + 185 = 0
:
Use the quadratic formula. a=12; b=97; c=185

You can do the math here and see the solutions are:
z = -5 and z = -3.0833:
:
we have to be careful when there are unknowns in the denominator of the original equation to avoid dividing by 0.
:
Notice in the expression , if we substitute -5 for z we get a 0 in the denominator so that can't be a solution. The only solution is -3.0833
Try substituting -3.0833 for z in the original equation to see if equality is present.
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