```Question 200142

{{{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:

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 = (-(-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.

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