To solve the quadratic equation 6x² + 10x = 0, we can start by factoring out the common terms.
1. **Factor the Equation**: First, we can factor out the common coefficient:
6x² + 10x = 0
Distributing this gives:
2x(3x + 5) = 0
2. **Set Each Factor to Zero**: To find the solutions, we set each factor equal to zero:
2x = 0 and 3x + 5 = 0
3. **Solving Each Equation**:
For the first factor:
2x = 0
x = 0
For the second factor:
3x + 5 = 0
3x = -5
x = -\frac{5}{3}
4. **Solutions in Simplest Radical Form**: The solutions to the quadratic equation 6x² + 10x = 0 are:
- x = 0
- x = -\frac{5}{3}
Thus, we can conclude that the solutions in simplest radical form are:
- x = 0
- x = -\frac{5}{3}
We have successfully factored and solved the quadratic equation, revealing both solutions!