To solve the equation \((z + 2)(2z - 3) = 0\), we can use the zero-product property, which states that if the product of two factors is zero, at least one of the factors must be zero.
This gives us two equations to solve:
- \(z + 2 = 0\)
- \(2z - 3 = 0\)
Solving the first equation:
\[ z + 2 = 0 \] Subtract 2 from both sides: \[ z = -2 \]
Solving the second equation:
\[ 2z - 3 = 0 \] Add 3 to both sides: \[ 2z = 3 \] Now divide both sides by 2: \[ z = \frac{3}{2} \]
Therefore, the solutions are:
\[ z = -2 \quad \text{or} \quad z = \frac{3}{2} \]