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

Jasonbradley

2 min read

·

Jun 16, 2024

13

Share

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

This equation is a quadratic equation in factored form. To solve for the values of 'n', 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:

   • 2n + 3 = 0
   • n - 4 = 0

2. Solve for 'n' in each equation:

   • 2n = -3
     • n = -3/2
   • n = 4

Solutions

Therefore, the solutions to the equation (2n + 3)(n - 4) = 0 are n = -3/2 and n = 4.

Verification

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

• For n = -3/2:

  • (2 * (-3/2) + 3) * (-3/2 - 4) = 0
  • (0) * (-11/2) = 0
  • 0 = 0 (True)

• For n = 4:

  • (2 * 4 + 3) * (4 - 4) = 0
  • (11) * (0) = 0
  • 0 = 0 (True)

Since both solutions satisfy the original equation, we have confirmed that n = -3/2 and n = 4 are the correct solutions.