(4k+5)(k+1)=0 Answer

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (4k+5)(k+1) = 0

This equation represents a quadratic equation in factored form. To find the solutions, we can utilize the Zero Product Property.

The Zero Product 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:

   • 4k + 5 = 0
   • k + 1 = 0

2. Solve each equation for k:

   • 4k = -5
   • k = -5/4
   • k = -1

Therefore, the solutions to the equation (4k+5)(k+1) = 0 are k = -5/4 and k = -1.

Verification:

We can verify our solutions by substituting each value of k back into the original equation.

• For k = -5/4:

  • (4(-5/4) + 5)(-5/4 + 1) = (0)(-1/4) = 0

• For k = -1:

  • (4(-1) + 5)(-1 + 1) = (1)(0) = 0

Both solutions satisfy the original equation.