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

2 min read Jun 17, 2024
(x-4)(2x+3)=0

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

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

  1. Set each factor equal to zero:

    • x - 4 = 0
    • 2x + 3 = 0

  2. Solve for x in each equation:

    • x = 4
    • 2x = -3
    • x = -3/2

Solutions

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

  • x = 4
  • x = -3/2

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

Verification

We can verify our solutions by substituting them back into the original equation:

  • For x = 4: (4 - 4)(2(4) + 3) = (0)(11) = 0
  • For x = -3/2: (-3/2 - 4)(2(-3/2) + 3) = (-11/2)(0) = 0

Since both solutions result in 0, we have confirmed that they are indeed the correct solutions to the equation.

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