To simplify the expression \(6z^2 - 4z^2 + 3 + 10z^2 + 7\), we can combine like terms.
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Combine the \(z^2\) terms: \[ 6z^2 - 4z^2 + 10z^2 = (6 - 4 + 10)z^2 = 12z^2 \]
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Combine the constant terms: \[ 3 + 7 = 10 \]
Now put it all together: \[ 12z^2 + 10 \]
Thus, the simplified expression is: \[ \boxed{12z^2 + 10} \]