Question 1131704

Solve 

{{{6x^4 -35x^3 + 62x^2 -35x + 6 = 0 }}}....factor completely

write {{{-35x^3}}} as {{{-2x^3-3x^3-12x^3-18x^3}}}
and  {{{62x^2}}} as {{{+x^2+4x^2+6x^2+6x^2+9x^2+36x^2}}}


{{{6x^4-2x^3-3x^3-12x^3-18x^3+x^2+4x^2+6x^2+6x^2+9x^2+36x^2-3x-2x-12x-18x+6}}}...group


{{{(6x^4-18x^3)-(2x^3-6x^2)-(3x^3-9x^2)-(12x^3-36x^2)+(4x^2-12x)-(2x-6)+(x^2-3x)
+(6x^2-18x)}}}


{{{6x^3(x-3)-2x^2(x-3)-3x^2(x-3)-12x^2(x-3)+4x(x-3)-2(x-3)+x(x-3)
+6x(x-3)}}}

{{{(x-3)(6x^3-2x^2-3x^2-12x^2+4x-2+x+6x)}}}

{{{(x-3)((6x^3-12x^2)-(2x^2-4x)-(3x^2-6x)+(x-2))}}}

{{{(x-3)(6x^2(x-2)-2x(x-2)-3x(x-2)+(x-2))}}}

{{{(x-3)(x-2)(6x^2-2x-3x+1)}}}

{{{(x-3)(x-2)((6x^2-3x)-(2x-1))}}}

{{{(x-3)(x-2)(3x(2x-1)-(2x-1))}}}

{{{(x - 3) (x - 2) (2x - 1) (3 x - 1) = 0}}}


solutions:

{{{x=3}}}
{{{x=2}}}
{{{x=1/2}}}
{{{x=1/3}}}


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