Question 228522
Solve for x using the factoring method: {{{18x^3=2x}}}


Step 1.  Subtract 2x from both sides of the equation


{{{18x^3-2x=2x-2x}}}


{{{18x^3-2x=0}}}


Step 2.  Look at the numbers which has 2 as a common factor.  Then,


{{{2(9x^3-x)=0}}}


Step 3.  Look at the variable x which has x as a common factor. Then,


{{{2x(9x^2-1)=0}}}.


Step 4.  But {{{9x^2-1=9x^2-1^2=(3x-1)(3x+1)}}} which is recognized as the difference of squares.  As a result we have,


{{{2x(9x^2-1)=2x(3x-1)(3x+1)=0}}}


Step 5.  This implies {{{x=0}}}, {{{3x-1=0}}} and {{{3x+1=0}}}.


Add 1 to both sides of {{{3x-1=0}}} to get {{{3x=1}}}. 


Divide by 3 to both sides of the equation to get {{{x=1/3}}}


Subtract 1 to both sides of {{{3x+1=0}}} to get {{{3x=-1}}}


Divide by 3 to both sides of the equation to get  {{{x=-1/3}}}


Step 6.  ANSWER:  The solution is {{{x=0}}}, {{{x=-1/3}}} and {{{x=1/3}}}.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J