SOLUTION: -6x^3-11x^2+2x=0

Question 290067: -6x^3-11x^2+2x=0
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
It would be helpful if you included the instructions for the problem. Like your problem, for example, the instructions probably say "Solve" or "Find the solution(s) to this equation" or something like that. Tutors are more likely to help when the problem is clear.

Assuming the problem is to solve the equation...

This equation is a polynomial of degree (highest exponent) 3. Solving an equation of this type involves getting one side equal to zero and then factoring. Your equation already has one side equal to zero so we can proceed to the factoring.

When factoring always start with the Greatest Common Factor (GCF). The GCF here is "x":

Now we try other factoring techniques to factor the second factor, if possible. The second factor does not fit any of the factoring patterns. But it is a trinomial that will factor. (Note: if you can't see how to factor it or if it doesn't factor at all, we can use the Quadratic Formula on it.)

None of these factors will factor further so we are ready to move on. By the Zero Product Property we know that this product can be zero only if one of the factors is zero. So:
x = 0 or -6x+1 = 0 or x+2 = 0
Solving these we get:
x = 0 or x = 1/6 or x = -2
A degree 3 polynomial has three solutions so these are all the solutions to your equation. You can check them by substituting them, one at a time, into the original equation to see if the numbers fit.

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