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3(2f + 5) = 6 - 4f - 21

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To solve the equation \( 3(2f + 5) = 6 - 4f - 21 \), follow these steps:

  1. Start by simplifying both sides of the equation.

    Left-hand side: \[ 3(2f + 5) = 6f + 15 \]

    Right-hand side: \[ 6 - 4f - 21 = -4f - 15 \]

    So the equation now looks like: \[ 6f + 15 = -4f - 15 \]

  2. Next, combine like terms. Add \( 4f \) to both sides: \[ 6f + 4f + 15 = -15 \] Which simplifies to: \[ 10f + 15 = -15 \]

  3. Now, subtract 15 from both sides: \[ 10f = -15 - 15 \] Simplifying gives: \[ 10f = -30 \]

  4. Finally, divide both sides by 10: \[ f = -3 \]

So the solution is: \[ \boxed{-3} \]