Answer :

Final answer:

The equation, 19x^(3) + 7x^(2) = x^(2) - x^(3), can be solved by rearranging, combining like terms, factoring, and setting each factor equal to zero. The solutions to the equation are x = 0 and x = -3/10.

Explanation:

This question is asking you to solve the equation 19x^(3) + 7x^(2) = x^(2) - x^(3). Let's break this down into steps:

  1. Firstly, rearrange the equation to bring all terms to one side of the equation. This gives you 19x^(3) + x^(3) + 7x^(2) - x^(2) = 0
  2. Consolidate like terms: This simplifies to 20x^(3) + 6x^(2) = 0
  3. Factor out the common factor, in this case, 2x^(2). This leaves you with 2x^(2)(10x + 3) = 0
  4. Finally, set each factor equal to zero to find the solution. This gives you x = 0 and x = -3/10. These are your solutions.

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