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$3(5z + 8) = -21$
Step1: Divide both sides by 3
$\frac{3(5z + 8)}{3} = \frac{-21}{3}$
$5z + 8 = -7$
Step2: Subtract 8 from both sides
$5z + 8 - 8 = -7 - 8$
$5z = -15$
Step3: Divide both sides by 5
$\frac{5z}{5} = \frac{-15}{5}$
$z = -3$
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$z = -3$