To solve the quadratic equation 6x² + 24x = 0, we can start by factoring the expression. First, we notice that both terms on the left side of the equation have a common factor of 6x. Thus, we can factor out 6x:
6x(x + 4) = 0
Once we have factored the equation, we can set each factor equal to zero to find the solutions:
- 6x = 0
- x + 4 = 0
For the first factor, 6x = 0, we can divide both sides by 6:
x = 0
For the second factor, x + 4 = 0, we can subtract 4 from both sides:
x = -4
Thus, the solutions to the quadratic equation 6x² + 24x = 0 are:
- x = 0
- x = -4
In summary, we found that the solutions are x = 0 and x = -4. These are the values of x that make the original equation true.