To evaluate the expression \( 3z^2 + 6z + 9 \) when \( z = 6 \), we can simply substitute \( z \) with \( 6 \) in the expression.
First, let's clarify that there seems to be a small mix-up in your phrasing with "when z, equals, 6z=6." Assuming you meant \( z = 6 \), we proceed with the calculations.
Now, substituting \( z = 6 \):
\[ 3(6^2) + 6(6) + 9 \]
Calculating each term step by step:
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Calculate \( 6^2 \): \[ 6^2 = 36 \]
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Multiply by 3: \[ 3(36) = 108 \]
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Calculate \( 6(6) \): \[ 6(6) = 36 \]
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Now add all the terms together: \[ 108 + 36 + 9 \]
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First, add \( 108 + 36 \): \[ 108 + 36 = 144 \]
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Now, add \( 144 + 9 \): \[ 144 + 9 = 153 \]
Therefore, the value of the expression \( 3z^2 + 6z + 9 \) when \( z = 6 \) is \( \boxed{153} \).
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