To solve the equation \( 5x + 6 = 2x - 21 \), follow these steps:
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Move all terms involving \( x \) to one side of the equation. You can do this by subtracting \( 2x \) from both sides:
\[ 5x - 2x + 6 = -21 \]
This simplifies to:
\[ 3x + 6 = -21 \]
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Next, move the constant term to the other side by subtracting 6 from both sides:
\[ 3x = -21 - 6 \]
Simplifying gives:
\[ 3x = -27 \]
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Now, divide both sides by 3 to isolate \( x \):
\[ x = \frac{-27}{3} \]
This simplifies to:
\[ x = -9 \]
So the solution to the equation \( 5x + 6 = 2x - 21 \) is:
\[ \boxed{-9} \]
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