Question 363157
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Hi, 
substituion verifies that 1/2 is a root (1 - 3 + 3 - 1 = 0)

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          8x^2 -   8x +     2
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(x -.5) | 8x^3 -  12x^2 +   6x - 1
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applying quadratic equation
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (8 +- sqrt( 8^2-64 ))/(16) }}}
x = 1/2
factoring {{{8x^3-12x^2+6x-1}}} would result as: 
(x-.5)(x -.5)(x -.5)