Solve the quadratic equation $2d^2 - 5d = 3$ by applying the factoring method.

Step 1 — Write in standard form. Subtract $3$ from both sides: $2d^2 - 5d - 3 = 0$

Step 2 — Factor the quadratic expression. $(2d + 1)(d - 3) = 0$

Step 3 — Apply the Zero Product Property. Set each factor equal to zero: $2d + 1 = 0 \quad \text{or} \quad d - 3 = 0$

Step 4 — Solve each linear equation: $d = -\frac{1}{2} \quad \text{or} \quad d = 3$

Step 5 — Check both solutions by substituting into the original equation $2d^2 - 5d = 3$: For $d = -\frac{1}{2}$: $2\left(-\frac{1}{2}\right)^2 - 5\left(-\frac{1}{2}\right) = 2\left(\frac{1}{4}\right) + \frac{5}{2} = \frac{1}{2} + \frac{5}{2} = 3$ ✓ For $d = 3$: $2(3)^2 - 5(3) = 18 - 15 = 3$ ✓ The solutions are $d = -\frac{1}{2}$ and $d = 3$.