$a)$

$3x^3+27=51\mid -27$

$3x^3=24\mid :3$

$x^3=8$

$x=\sqrt[3]{8}=2$

 

 

$b)$

$64x^3+7=8\mid -7$

$64x^3=1\mid :64$

$x^3=\frac{1}{64}$

$x=\sqrt[3]{\frac{1}{64}}=\frac{1}{4}$

 

 

 

$c)$

$2x^3+300=50\mid -300$

$2x^3=-250\mid :2$

$x^3=-125$

$x=\sqrt[3]{-125}=-5$

 

 

 

$d)$

$27x^3+9=8\mid -9$

$27x^3=-1\mid :27$

$x^3=-\frac{1}{27}$

$x=\sqrt[3]{-\frac{1}{27}}=-\frac{1}{3}$

 

 

 

$e)$

$x\left(x^2+2\right)=2\left(x+32\right)$

$x^3+2x=2x+64\mid -2x$

$x^3=64$

$x=\sqrt[3]{64}=4$

 

 

 

$f)$

$x\left(x^2-4\right)=-4\left(x+2\right)$

$x^3-4x=-4x-8\mid +4x$

$x^3=-8$

$x=\sqrt[3]{-8}$

$x=-2$