(4-x)(x+5)(2x-3)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (4-x)(x+5)(2x-3)=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 several factors is equal to zero, at least one of the factors must be zero.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • 4 - x = 0
   • x + 5 = 0
   • 2x - 3 = 0

2. Solve each equation for x:

   • x = 4
   • x = -5
   • x = 3/2

Solutions

Therefore, the solutions to the equation (4-x)(x+5)(2x-3) = 0 are:

• x = 4
• x = -5
• x = 3/2

These solutions represent the points where the graph of the cubic function intersects the x-axis.