Questions: Solve the equation. b(4b+5)(5b+4)=0

Solve the equation. b(4b+5)(5b+4)=0
Transcript text: Solve the equation. \[ b(4 b+5)(5 b+4)=0 \]
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Solution

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Solution Steps

Step 1: Set each factor equal to zero

Given the equation \( b(4b + 5)(5b + 4) = 0 \), we set each factor equal to zero: \[ b = 0 \] \[ 4b + 5 = 0 \] \[ 5b + 4 = 0 \]

Step 2: Solve for \( b \) in each equation

Solve each equation for \( b \):

  1. \( b = 0 \)
  2. \( 4b + 5 = 0 \) \[ 4b = -5 \] \[ b = -\frac{5}{4} \]
  3. \( 5b + 4 = 0 \) \[ 5b = -4 \] \[ b = -\frac{4}{5} \]

Final Answer

The solution set is: \[ \left\{ 0, -\frac{5}{4}, -\frac{4}{5} \right\} \]

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