Question 474361
{{{ -1*x^2 + 12x - 32 }}}
Set this equal to zero. ( note that there is no
equation until an = sign appears)
{{{ -1*x^2 + 12x - 32 = 0 }}}
Now it's an equation, and I can solve for {{{x}}}
I'll use the quadratic formula.
If the equation is in the form 
{{{ ax^2 + b*x + c = 0 }}}, then
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = -1 }}}
{{{ b = 12 }}}
{{{ c = -32 }}}
{{{x = (-12 +- sqrt( 12^2-4*(-1)*(-32) ))/(2*(-1)) }}} 
{{{x = (-12 +- sqrt( 144 - 128 ))/(-2) }}} 
{{{x = (-12 +- sqrt( 16 ))/(-2) }}} 
{{{x = (-12 + 4)/(-2) }}} 
{{{ x = -8/(-2) }}}
(1) {{{ x = 4 }}}
and
{{{x = (-12 - 4)/(-2) }}}
{{{ x = -16/(-2) }}}
(2) {{{ x = 8 }}}
These are the 2 solutions
Rewrite (1) and (2) as:
(1) {{{ x - 4 = 0 }}}
(2) {{{ x - 8 = 0 }}}
Now multiply both sides of (1) by {{{-1}}}
(1) {{{ -x + 4 = 0 }}}
Multiply (1) and (2) to get your equation
{{{ (-x + 4)*(x - 8) = -1*x^2 + 4x + 8x - 32 }}}
{{{ (-x + 4)*(x - 8) = -1*x^2 + 12x - 32 }}}
OK