Question 204049
I'll say {{{x = c^2}}}, then
{{{63c^4+36c^2-18 = 63X^2 + 36X - 18}}}
To find factors,
{{{63x^2 + 36x - 18 = 0}}}
Divide both sides by {{{9}}}
{{{7x^2 + 4x - 2 = 0}}}
quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 7}}}
{{{b = 4}}}
{{{c = -2}}}
{{{x = (-4 +- sqrt( 4^2-4*7*(-2) ))/(2*7) }}}
{{{x = (-4 +- sqrt( 16 + 56 ))/14 }}}
{{{x = (-4 +- sqrt( 72 ))/14 }}}
{{{x = (-4 +- 6*sqrt( 2 ))/14 }}}
{{{x = (-2 + 3*sqrt( 2 ))/7 }}}
and
{{{x = (-2 - 3*sqrt( 2 ))/7 }}}
And, since {{{x = c^2}}},
{{{c = sqrt((-2 - 3*sqrt( 2 ))/7) }}}

also
{{{c = sqrt((-2 + 3*sqrt( 2 ))/7) }}}
The factors are:
{{{c - sqrt((-2 - 3*sqrt( 2 ))/7) }}},
{{{c + sqrt((-2 - 3*sqrt( 2 ))/7) }}},
{{{c - sqrt((-2 + 3*sqrt( 2 ))/7) }}}
{{{c + sqrt((-2 + 3*sqrt( 2 ))/7) }}}
Unless I goofed, but I think method is OK