Questions: Solve. -4(y+7)(-y-6)=0 (If there is more than one solution, separate them with commas.) y=

Solve. -4(y+7)(-y-6)=0 (If there is more than one solution, separate them with commas.) y=
Transcript text: Solve. \[ -4(y+7)(-y-6)=0 \] (If there is more than one solution, separate them with commas.) \[ y= \]
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Solution

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Solution Steps

To solve the equation \(-4(y+7)(-y-6)=0\), we need to find the values of \(y\) that make the equation true. Since the product of the terms equals zero, at least one of the terms must be zero. Therefore, we set each factor equal to zero and solve for \(y\).

  1. Set \(y+7 = 0\) and solve for \(y\).
  2. Set \(-y-6 = 0\) and solve for \(y\).
Step 1: Set Each Factor to Zero

To solve the equation \(-4(y+7)(-y-6)=0\), we set each factor equal to zero:

  1. \(y + 7 = 0\)
  2. \(-y - 6 = 0\)
Step 2: Solve for \(y\)

Solving the first equation: \[ y + 7 = 0 \implies y = -7 \]

Solving the second equation: \[ -y - 6 = 0 \implies -y = 6 \implies y = -6 \]

Final Answer

The solutions to the equation are: \[ \boxed{y = -7, -6} \]

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