Questions: Solve for x (x+4)(x-3)=0

Solve for x (x+4)(x-3)=0
Transcript text: Solve for $x$ \[ (x+4)(x-3)=0 \]
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Solution

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Solution Steps

To solve the equation \((x+4)(x-3)=0\), we can use the zero-product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for \(x\).

Step 1: Apply the Zero-Product Property

Given the equation \((x+4)(x-3)=0\), we apply the zero-product property. This property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

  1. \(x + 4 = 0\)
  2. \(x - 3 = 0\)
Step 2: Solve Each Equation

Solve each equation for \(x\):

  1. For \(x + 4 = 0\): \[ x = -4 \]

  2. For \(x - 3 = 0\): \[ x = 3 \]

Final Answer

\(\boxed{x = -4, \, x = 3}\)

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