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(x−7)(x+5)(2x−3)=0

2 min read Jun 17, 2024
(x−7)(x+5)(2x−3)=0

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

This equation is a cubic equation, meaning it has a highest power of 3. Solving cubic equations can be complex, but this specific equation is set up for an easy solution.

The Zero Product Property

The equation is already factored, and we can take advantage of the Zero Product Property. This property states that if the product of several factors is equal to zero, then at least one of the factors must be equal to zero.

Therefore, to solve the equation, we need to set each factor equal to zero and solve for x:

  1. (x - 7) = 0 Adding 7 to both sides, we get x = 7

  2. (x + 5) = 0 Subtracting 5 from both sides, we get x = -5

  3. (2x - 3) = 0 Adding 3 to both sides and then dividing by 2, we get x = 3/2

The Solutions

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

  • x = 7
  • x = -5
  • x = 3/2

These are the values of x that make the equation true.

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