If x = p is a solution of the equation x(2x + 5) = 3, then find the values of p.

If x = p is a solution of the equation x(2x + 5) = 3 , then x = p satisfies the equation.
Putting x = p in equation,

$p(2p + 5) = 3 \\[0.5em] \Rightarrow 2p^2 + 5p = 3 \\[0.5em] \Rightarrow 2p^2 + 5p - 3 = 0 \\[0.5em] \Rightarrow 2p^2 + 6p - p - 3 = 0 \\[0.5em] \Rightarrow 2p(p + 3) - 1(p + 3) = 0 \\[0.5em] \Rightarrow (2p - 1)(p + 3) = 0 \text{ (Factorising left side) }\\[0.5em] \Rightarrow 2p - 1 = 0 \text{ or } p + 3 = 0 \text{ (Zero-product rule) } \\[0.5em] \Rightarrow 2p = 1 \text{ or } p = -3 \\[0.5em] p = \dfrac{1}{2} \text{ or } p = -3$

Hence, the values of p are -3 , $\dfrac{1}{2}$.