Answer
The solutions are 0 and 7.
Work Step by Step
$x^{3}$-14$x^{2}$+49x=0
x($x^{2}$-14$x^{}$+49)=0
x($x^{2}$-7$x^{}$-7x+49)=0
x[x(x-7)-7(x-7)]=0
x(x-7)(x-7)=0
x=0 or x-7=0 or x-7=0
x=0 or x=7 or x=7
The solutions are 0 and 7.
Check
Let x=0
$x^{3}$-14$x^{2}$+49x=0
$0^{3}$-14*$0^{2}$+49*0=0
0-0+0=0
0=0
Let x=7
$x^{3}$-14$x^{2}$+49x=0
$7^{3}$-14*$7^{2}$+49*7=0
343-14*49+343=0
343-686+343=0
686-686=0
0=0
