What are the solutions for the equation 3x^2 + 22x = 0?

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To find the solutions for the equation 3x^2 + 22x = 0, we can start by factoring the equation. First, we notice that there is a common factor in both terms:

3x^2 + 22x = 0

We can factor out x from the equation:

x(3x + 22) = 0

Now we have a product equal to zero, which tells us that at least one of the factors must also be zero. This gives us two cases to consider:

  1. x = 0
  2. 3x + 22 = 0

For the first case:

x = 0

For the second case, we solve for x:

Subtracting 22 from both sides results in:

3x = -22

Dividing both sides by 3 gives:

x = -\frac{22}{3}

Now, we can summarize the solutions we found:

The two solutions to the equation 3x^2 + 22x = 0 are:

  • x = 0
  • x = -\frac{22}{3}

Thus, the equation has two solutions.

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