d. \( 2 x^{2}-7 x-9=(2 x+9)(x-2) \)

To solve the equation \( 2x^2 - 7x - 9 = (2x + 9)(x - 2) \), we first need to expand the right-hand side. Starting with the right-hand side: \[ (2x + 9)(x - 2) = 2x \cdot x + 2x \cdot (-2) + 9 \cdot x + 9 \cdot (-2) \] Calculating each term: \[ = 2x^2 - 4x + 9x - 18 \] Combining like terms: \[ = 2x^2 + 5x - 18 \] Now, we can rewrite the original equation: \[ 2x^2 - 7x - 9 = 2x^2 + 5x - 18 \] Next, we subtract \( 2x^2 \) from both sides: \[ -7x - 9 = 5x - 18 \] Now, we can move all terms involving \( x \) to one side and constant terms to the other side. Adding \( 7x \) to both sides gives: \[ -9 = 5x + 7x - 18 \] This simplifies to: \[ -9 = 12x - 18 \] Next, we add \( 18 \) to both sides: \[ -9 + 18 = 12x \] This simplifies to: \[ 9 = 12x \] Now, we divide both sides by \( 12 \): \[ x = \frac{9}{12} = \frac{3}{4} \] Thus, the solution to the equation is: \[ \boxed{\frac{3}{4}} \]