Question

Find the solution set for (3x-4)(7x+3)=0

Answer 1

To find the solution set for the equation \((3x-4)(7x+3)=0\), we need to set each factor equal to zero and solve for \(x\).

1. **Set the first factor to zero**:
\[
3x - 4 = 0
\]
Adding 4 to both sides:
\[
3x = 4
\]
Dividing by 3:
\[
x = \frac{4}{3}
\]

2. **Set the second factor to zero**:
\[
7x + 3 = 0
\]
Subtracting 3 from both sides:
\[
7x = -3
\]
Dividing by 7:
\[
x = -\frac{3}{7}
\]

Now, we have found both solutions. Thus, the solution set is:
\[
\left\{ \frac{4}{3}, -\frac{3}{7} \right\}
\]