Question 200142
{{{3x^2-6x=0}}} Start with the given equation.



{{{3x(x-2)=0}}} Factor out the GCF 3x



{{{3x=0}}} or {{{x-2=0}}} Set each factor equal to zero



{{{x=0}}} or {{{x=2}}} Solve for x in each equation



So the solutions are {{{x=0}}} or {{{x=2}}}



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Here's another way to solve the equation:





{{{3x^2-6x=0}}} Start with the given equation.




Notice that the quadratic {{{3x^2-6x}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=-6}}}, and {{{C=0}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-6) +- sqrt( (-6)^2-4(3)(0) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-6}}}, and {{{C=0}}}



{{{x = (6 +- sqrt( (-6)^2-4(3)(0) ))/(2(3))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{x = (6 +- sqrt( 36-4(3)(0) ))/(2(3))}}} Square {{{-6}}} to get {{{36}}}. 



{{{x = (6 +- sqrt( 36-0 ))/(2(3))}}} Multiply {{{4(3)(0)}}} to get {{{0}}}



{{{x = (6 +- sqrt( 36 ))/(2(3))}}} Subtract {{{0}}} from {{{36}}} to get {{{36}}}



{{{x = (6 +- sqrt( 36 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (6 +- 6)/(6)}}} Take the square root of {{{36}}} to get {{{6}}}. 



{{{x = (6 + 6)/(6)}}} or {{{x = (6 - 6)/(6)}}} Break up the expression. 



{{{x = (12)/(6)}}} or {{{x =  (0)/(6)}}} Combine like terms. 



{{{x = 2}}} or {{{x = 0}}} Simplify. 



So the solutions are {{{x = 2}}} or {{{x = 0}}} (note: the order of the solutions does NOT matter)



So either way, we get the same answer.