Answer
$x=0$ and $x=3$.
Work Step by Step
The given equation is
$\Rightarrow 5x^2-15x=0$
Factor out $5x$.
$\Rightarrow 5x(x-3)=0$
Use zero-product property rule.
$\Rightarrow 5x=0$ or $x-3=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=3$
Check:-
$x=0$
$\Rightarrow 5(0)^2-15(0)=0$
$\Rightarrow 5(0)-15(0)=0$
$\Rightarrow 0=0$
True.
Check:-
$x=3$
$\Rightarrow 5(3)^2-15(3)=0$
$\Rightarrow 5(9)-15(3)=0$
$\Rightarrow 45-45=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $x=0$ and $x=3$.
