Question 535922
Write the opposite way
{{{ -12x^2 + 31x - 20 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -12 }}}
{{{ b = 31 }}}
{{{ c = -20 }}}
{{{x = ( -31 +- sqrt( 31^2 - 4*(-12)*(-20) ))/(2*(-12)) }}}
{{{x = ( -31 +- sqrt( 961 - 960 ))/-24 }}}
{{{x = ( -31 +- sqrt( 1 ))/-24 }}}
{{{x = ( -31 + 1 ) / -24 }}}
{{{x = -30/-24 }}}
{{{ x = 5/4 }}}
and
{{{x = ( -31 - 1 ) / -24 }}} 
{{{ x = -32/-24 }}}
{{{ x = 4/3 }}}
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I can also say
{{{ -x = -(5/4) }}}
(1) {{{ -x + 5/4 = 0 }}}
multiply both sides by {{{4}}}
(1) {{{ -4x + 5 = 0 }}}
and
{{{ x = 4/3 }}}
(2) {{{ x - 4/3 = 0 }}}
multiply both sides by {{{3}}}
(2) {{{ 3x - 4 = 0 }}}
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Multiply (1) and (2)
{{{ (-4x + 5)*(3x - 4) = 0 }}}
{{{ -12x^2 + 31x - 20 = 0}}}
So, the factors are
{{{ -4x + 5 }}}
and
{{{ 3x - 4 }}}