To simplify the expression \(-h^2 + 5h^2 - 6h^2\), we can combine the like terms:
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Start with the coefficients of \(h^2\): \[ -1 + 5 - 6 \]
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Calculate it step by step: \[ -1 + 5 = 4 \] \[ 4 - 6 = -2 \]
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Thus, the combined coefficient of \(h^2\) is \(-2\).
Now, we can write the simplified expression: \[ -2h^2 \]
Therefore, the simplified expression is: \[ \boxed{-2h^2} \]