To solve the equation \(-3x^2 - 21x - 30 = 0\), we can start by simplifying it. First, we can divide the whole equation by \(-3\) to make it easier to work with:
\[ x^2 + 7x + 10 = 0 \]
Next, we can factor this quadratic equation. We need to find two numbers that multiply to \(10\) (the constant term) and add up to \(7\) (the coefficient of \(x\)). The numbers \(2\) and \(5\) fit this requirement.
Thus, we can factor the equation as:
\[ (x + 2)(x + 5) = 0 \]
Setting each factor equal to zero gives us the solutions:
- \(x + 2 = 0 \Rightarrow x = -2\)
- \(x + 5 = 0 \Rightarrow x = -5\)
Therefore, the solutions to the equation \(-3x^2 - 21x - 30 = 0\) are:
\[ x = -2 \quad \text{and} \quad x = -5 \]