solve \( 3 h^{2}=-12 h \)

To solve the equation \( 3h^{2} = -12h \), follow these steps: ### Step 1: Rewrite the Equation in Standard Form Move all terms to one side to set the equation to zero: \[ 3h^{2} + 12h = 0 \] ### Step 2: Factor Out the Greatest Common Factor (GCF) Identify and factor out the GCF from the terms: \[ 3h(h + 4) = 0 \] ### Step 3: Apply the Zero Product Property If the product of two factors is zero, at least one of the factors must be zero: \[ 3h = 0 \quad \text{or} \quad h + 4 = 0 \] ### Step 4: Solve for \( h \) in Each Case 1. **First Equation:** \( 3h = 0 \) \[ h = 0 \] 2. **Second Equation:** \( h + 4 = 0 \) \[ h = -4 \] ### **Solution** The solutions to the equation \( 3h^{2} = -12h \) are: \[ h = 0 \quad \text{and} \quad h = -4 \]