Question 300474
You can factor,
{{{2a^2 - 5a - 12 =(2a+3)(a-4)}}}
Two solutions:
{{{2a+3=0}}}
{{{2a=-3}}}
{{{highlight_green( a=-3/2)}}}
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{{{a-4=0}}}
{{{highlight_green(a=4)}}}
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Graphical verification,

{{{ graph( 300, 300, -5, 5, -5, 5, 2x^2 - 5x - 12 ) }}}