(x+3)(x-4)(2x+1)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+3)(x-4)(2x+1) = 0

This equation is a cubic equation, meaning it has a highest power of x of 3. To solve it, we can use the Zero Product Property:

Zero Product Property

If the product of several factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

In our equation, we have three factors:

• (x+3)
• (x-4)
• (2x+1)

To make the product equal to zero, at least one of these factors must be zero. So, we set each factor equal to zero and solve for x:

• x + 3 = 0

  • x = -3

• x - 4 = 0

  • x = 4

• 2x + 1 = 0

  • 2x = -1
  • x = -1/2

Solutions

Therefore, the solutions to the equation (x+3)(x-4)(2x+1) = 0 are:

• x = -3
• x = 4
• x = -1/2

Graphing the Equation

The graph of this equation will intersect the x-axis at these three points, representing the solutions:

• (-3, 0)
• (4, 0)
• (-1/2, 0)