(x-7)(x+5)(2x-3)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-7)(x+5)(2x-3) = 0

This equation represents a cubic polynomial set equal to zero. To find the solutions, we can utilize the Zero Product Property: If the product of multiple factors is zero, then at least one of those factors must be zero.

Let's break down the equation and solve for each factor:

Factor 1: (x-7) = 0

• Add 7 to both sides: x = 7

Factor 2: (x+5) = 0

• Subtract 5 from both sides: x = -5

Factor 3: (2x-3) = 0

• Add 3 to both sides: 2x = 3
• Divide both sides by 2: x = 3/2

Therefore, the solutions to the equation (x-7)(x+5)(2x-3) = 0 are x = 7, x = -5, and x = 3/2.

These solutions represent the x-intercepts of the cubic function represented by the equation.