Solve.
\[
p+\frac{3}{p}=-4
\]

Step 1 ：Multiply the entire equation by \(p\) to get rid of the fraction: \(p^2 + 3 = -4p\)

Step 2 ：Rearrange the equation to set it equal to zero: \(p^2 + 4p + 3 = 0\)

Step 3 ：Factor the equation: \((p + 1)(p + 3) = 0\)

Step 4 ：Set each factor equal to zero and solve for \(p\): \(p + 1 = 0\) or \(p + 3 = 0\), which gives \(p = -1\) or \(p = -3\)

Step 5 ：Check the solutions by substituting them back into the original equation. For \(p = -1\): \(-1 + \frac{3}{-1} = -1 - 3 = -4\). For \(p = -3\): \(-3 + \frac{3}{-3} = -3 - 1 = -4\)

Step 6 ：\(\boxed{p = -1, -3}\) are the solutions to the equation \(p+\frac{3}{p}=-4\)