To solve the equation \(3x^2 - 30x - 72 = 0\), we can either factor the equation or use the quadratic formula. In this case, let's try factoring.
First, we can simplify the equation by dividing all terms by 3:
\[ x^2 - 10x - 24 = 0 \]
Next, we look for two numbers that multiply to \(-24\) (the constant term) and add to \(-10\) (the coefficient of the linear term). The numbers \(-12\) and \(2\) work because:
\[ -12 \times 2 = -24 \] \[ -12 + 2 = -10 \]
We can factor the quadratic as follows:
\[ (x - 12)(x + 2) = 0 \]
Setting each factor equal to zero gives us the solutions:
\[ x - 12 = 0 \quad \Rightarrow \quad x = 12 \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \]
Now, looking at the options provided:
- A) \(x = -12\)
- B) \(x = -4\)
- C) \(x = -2\) (which is a solution)
- D) \(x = -6\)
The value of \(x\) that is a solution to the equation is:
\[ \boxed{-2} \]