First, bring everything to one side of the equation:
#3x^2=-9x#
#3x^2color(blue)+color(blue)(9x)=-9xcolor(blue)+color(blue)(9x)#
#3x^2color(blue)+color(blue)(9x)=color(red)cancelcolor(black)(color(black)-9xcolor(blue)+color(blue)(9x))#
#3x^2+9x=0#
Now, divide by the common factor #3#:
#color(blue)(color(black)(3x^2+9x)/3)=color(blue)(color(black)0/3)#
#color(blue)(color(black)(color(red)cancelcolor(black)3x^2+color(red)cancelcolor(black)9^3x)/color(red)cancelcolor(blue)3)=color(blue)(color(black)0/3)#
#x^2+3x=color(blue)(color(black)0/3)#
#x^2+3x=0#
Now, use the distributive property backward to factor out the #x# term:
#color(red)x*color(blue)x+color(red)x*color(blue)3=0#
#(color(red)x)(color(blue)(x+3))=0#
Now, set each factor equal to #0# and solve for #x# in each one:
#color(white){color(black)(
(color(red)x=0,qquadcolor(blue)(x+3)=0),
(,qquadcolor(blue)x=-3):}#
These are the two solutions: #x=0# and #x=-3#. Hope this helped!
