SOLUTION: The sum of all the solutions of the equation: (10x−3a)(3x+39)(5x−3)=0 is (−1). Find a.

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Question 1067986: The sum of all the solutions of the equation: (10x−3a)(3x+39)(5x−3)=0 is (−1). Find a.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39631) About Me  (Show Source):
Answer by ikleyn(52932) About Me  (Show Source):
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The solutions are x = 3a%2F10, -39%2F3 = -13 and 3%2F5.


According to the condition, their sum is -1. It gives you an equation


3a%2F10+-+13+%2B+3%2F5 = -1,   or

3a%2F10+%2B+6%2F10 = -1 + 13,   or

%283a%2B6%29%2F10 = 12  --->  3a + 6 = 120  --->  3a = 114  --->  a = 114%2F3 = 38.

Solved. a = 38.