(x-2)(3x+5)(x^2-49)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-2)(3x+5)(x^2-49) = 0

This equation is a cubic equation, meaning it has a highest power of 3. To solve it, we can utilize the Zero Product Property. This property states that if the product of multiple factors equals zero, at least one of those factors must be zero.

Let's break down the equation:

• (x-2) is our first factor
• (3x+5) is our second factor
• (x^2-49) is our third factor

Applying the Zero Product Property, we set each factor equal to zero and solve for x:

Solving for x in each factor:

1. (x-2) = 0

• Add 2 to both sides: x = 2

2. (3x+5) = 0

• Subtract 5 from both sides: 3x = -5
• Divide both sides by 3: x = -5/3

3. (x^2-49) = 0

• Add 49 to both sides: x^2 = 49
• Take the square root of both sides: x = ±7

Therefore, the solutions to the equation (x-2)(3x+5)(x^2-49) = 0 are:

• x = 2
• x = -5/3
• x = 7
• x = -7

These are the four distinct values of x that satisfy the given equation.