Answer:
Values of x are: x=0 or x=-3 or x=-12
Step-by-step explanation:
The equation given to solve using zero product property is [tex]2x^3+30x^2+72x=0[/tex]
Zero property rule states that if ab=0 then a=0 or b=0
Taking x common from the equation:
[tex]2x^3+30x^2+72x=0\\x(2x^2+30x+72)=0\\[/tex]
Applying zero product rule
[tex]x(2x^2+30x+72)=0\\x=0 \ or \ 2x^2+30x+72=0[/tex]
Now, solving [tex]2x^2+30x+72=0[/tex]
Using quadratic formula to find value of x
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Putting values
[tex]$x=\frac{-30\pm\sqrt{(30)^2-4(2)(72)}}{2(2)}$\\$x=\frac{-30\pm\sqrt{324}}{4}$\\$x=\frac{-30\pm18}{4}$\\$x=\frac{-30+18}{4} \ or \ x=\frac{-30-18}{4}$ \\x=-3 \ or \ x=-12[/tex]
So, Values of x are: x=0 or x=-3 or x=-12
