SOLUTION: Please help me find the real number solutions of this equation: {{{ 18x^3=50x }}} Thank you!

Question 420033: Please help me find the real number solutions of this equation:

Thank you!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

In general, to solve equations where the variable has exponents larger than 1, you:

Get one side of the equation to be zero.
Factor the the other side.
Use the Zero Product Property.
Solve the equations from the Zero Product Property.

So we start by subtracting 50x from each side:

Now we factor. And factoring always starts with the Greatest Common Factor (GCF). The GCF is 2x:

The second factor is a difference of squares so it will factor according to the pattern:
2x(3x+5)(3x-5) = 0
We are finished factoring. The Zero Product Property tells us this (or any) product can be zero only if one (or more) of the factors is zero. So:
2x = 0 or 3x+5 = 0 or 3x-5 = 0
Solving each of these we get:
x = 0 or x = -5/3 or x = 5/3
These are the three real solutions to your equation.

P.S. "Exponential equations" are equations where the variable is in the exponent. Your equation is what is called a "Polynomial equation". Posting your problems under the right category may result in faster responses from the tutors.
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