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\frac{9}{5}z\times 5z+\frac{9}{5}z\left(-3\right)
Use the distributive property to multiply \frac{9}{5}z by 5z-3.
\frac{9}{5}z^{2}\times 5+\frac{9}{5}z\left(-3\right)
Multiply z and z to get z^{2}.
9z^{2}+\frac{9}{5}z\left(-3\right)
Cancel out 5 and 5.
9z^{2}+\frac{9\left(-3\right)}{5}z
Express \frac{9}{5}\left(-3\right) as a single fraction.
9z^{2}+\frac{-27}{5}z
Multiply 9 and -3 to get -27.
9z^{2}-\frac{27}{5}z
Fraction \frac{-27}{5} can be rewritten as -\frac{27}{5} by extracting the negative sign.
\frac{9}{5}z\times 5z+\frac{9}{5}z\left(-3\right)
Use the distributive property to multiply \frac{9}{5}z by 5z-3.
\frac{9}{5}z^{2}\times 5+\frac{9}{5}z\left(-3\right)
Multiply z and z to get z^{2}.
9z^{2}+\frac{9}{5}z\left(-3\right)
Cancel out 5 and 5.
9z^{2}+\frac{9\left(-3\right)}{5}z
Express \frac{9}{5}\left(-3\right) as a single fraction.
9z^{2}+\frac{-27}{5}z
Multiply 9 and -3 to get -27.
9z^{2}-\frac{27}{5}z
Fraction \frac{-27}{5} can be rewritten as -\frac{27}{5} by extracting the negative sign.