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Solve for `d`. `(d + 5)(d + 1) = 0` Write your answers as integers or as proper or improper fractions in simplest form. `d =` _____ or `d =` _____

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Solve a quadratic equation using the zero product propertyright chevron icon

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Q. Solve for `d`. `(d + 5)(d + 1) = 0` Write your answers as integers or as proper or improper fractions in simplest form. `d =` _____ or `d =` _____
  1. Factorizing the equation: The equation `(d + 5)(d + 1) = 0` is a product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for `d` separately.
  2. Setting the first factor equal to zero: First, set the first factor equal to zero: `d + 5 = 0`. To solve for `d,` we need to isolate `d` by subtracting `5` from both sides of the equation.
  3. Solving for `d` when the first factor is zero: After subtracting `5` from both sides, we get `d =` -5.
  4. Setting the second factor equal to zero: Now, set the second factor equal to zero: `d + 1 = 0`. Similarly, we will isolate `d` by subtracting `1` from both sides of the equation.
  5. Solving for `d` when the second factor is zero: After subtracting `1` from both sides, we get `d =` -1.
  6. Finding the solutions for `d:` We have found two solutions for `d: d = -5` and `d = -1`. These are the values of `d` that satisfy the original equation.

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