Answer
The solution set is $\{-2,5\}$.
Work Step by Step
The given expression is
$x(x-3)=10$
Clear the parentheses.
$x^2-3x=10$
Subtract $10$ from both sides.
$x^2-3x-10=10-10$
Simplify.
$x^2-3x-10=0$
Factor
$x^2-5x+2x-10=0$
$x(x-5)+2(x-5)=0$
$(x-5)(x+2)=0$
Set each factor equal to zero.
$x-5=0$ or $x+2=0$
Isolate $x$.
$x=5$ or $x=-2$.
