What is the solution set for the equation 7x² + 3x = 0?

To find the solution set for the equation 7x² + 3x = 0, we start by factoring out the common term:

Step 1: Factor the equation.

This equation can be factored as:

x(7x + 3) = 0

Here, we see that we can set each factor to zero to find the individual solutions.

Step 2: Solve for x.

We have two factors to set equal to zero:

From the first factor, we immediately find:

x = 0

For the second factor, we solve for x:

7x + 3 = 0

Subtract 3 from both sides:

7x = -3

Now, divide both sides by 7:

x = -3/7

Step 3: Write the solution set.

Combining these results, we conclude that the solution set for the equation 7x² + 3x = 0 is:

{ 0, -3/7 }

This means that x can either be 0 or -3/7. Therefore, the complete solution set is:

{ 0, -3/7 }