How do you solve for x in the equation 2/3x² + 4x = 0?

To solve for x in the equation 2/3x² + 4x = 0, we can follow these steps:

1. First, we can factor out the common term from the equation. Notice that both terms on the left-hand side include an x. We can factor x out:

x(2/3x + 4) = 0

2. Now, we set each factor equal to zero:
• x = 0
• 2/3x + 4 = 0
3. Next, we solve for x in the second equation:

To isolate x, we first subtract 4 from both sides:

2/3x = -4

4. Then, multiply both sides by the reciprocal of 2/3, which is 3/2:

x = -4 * (3/2)

x = -6

Combining both solutions, we find:

x = 0 or x = -6

In conclusion, the solutions to the equation 2/3x² + 4x = 0 are:

x = 0 and x = -6.