Pregunta
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The solutions are \( h = 0 \) and \( h = -4 \).
Solución
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:
\[
h = 0 \quad \text{and} \quad h = -4
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
To solve the equation \( 3 h^{2} = -12 h \), first, let's bring all terms to one side of the equation: \( 3 h^{2} + 12 h = 0 \). Now, we can factor out the common term: \( 3 h (h + 4) = 0 \). This gives us two possible solutions: 1. \( 3 h = 0 \) which simplifies to \( h = 0 \). 2. \( h + 4 = 0 \) which simplifies to \( h = -4 \). So, the solutions are \( h = 0 \) and \( h = -4 \).
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