#1#. Find the #color(blue)("G.C.F. (greatest common factor)")# between the two terms on the left side and factor.
#2c^4-6c^3=12c^2-36c#
#color(blue)(2c^3)(c-3)=12c^2-36c#
#2#. Repeat for the right side.
#color(blue)(2c^3)(c-3)=color(blue)(12c)(c-3)#
#3#. Since #(c-3)# appears on both sides of the equation, they cancel each other out.
#color(blue)(2c^3)color(red)cancelcolor(black)((c-3))=color(blue)(12c)##color(red)cancelcolor(black)((c-3))#
#color(blue)(2c^3)=color(blue)(12c)#
#4#. Find the #color(plum)("G.C.F.")# between the left and right side terms and factor both sides.
#color(plum)(2c)(c^2)=color(plum)(2c)(6)#
#5#. Cancel out the #2c# on both sides of the equation.
#color(red)cancelcolor(plum)(2c)(c^2)=color(red)cancelcolor(plum)(2c)(6)#
#c^2=6#
#6#. Solve for #c# taking the square root of both sides.
#sqrt(c^2)=sqrt(6)#
#color(green)(c=sqrt(6))#
