Question 225247
{{{8x^2-2=0}}} 
<pre><font size = 4 color = "indigo"><b>
Divide every term by 2

{{{8x^2/2-2/2=0}}}

{{{4x^2-1=0}}}

{{{(2x)^2-1^2=0}}}

{{{(2x-1)(2x+1)=0}}}

2x - 1 = 0      2x + 1 = 0
    2x = 1          2x = -1
     x = {{{1/2}}}          x ={{{-1/2}}} 

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{{{red(3)x^2-blue(5)x-green(12)=0}}}

Multiply {{{red(3)}}} by {{{green(-12)}}}, get {{{-36}}}

Think of two numbers that multiply to 
give you {{{-36}}} and add to give you {{{blue(-5)}}}.

Answer: {{{blue(-9)}}} and {{{blue(""+4)}}}

So use those numbers {{{blue(-9)}}} and {{{blue(""+4)}}}

to write the middle term {{{blue(-5x)}}} as {{{blue(-9x+4x)}}}

So

{{{red(3)x^2-blue(5)x-green(12)=0}}}

now becomes:

{{{red(3)x^2-blue(9x+4x)-green(12)=0}}}

Now out of the first two terms on the left 
factor out {{{3x}}}

{{{3x(x-3)+4x-12=0}}}

Out of the last two terms on the left 
factor out {{{""+4}}}

{{{3x(x-3)+4(x-3)=0}}}

Notice that {{{red((x-3))}}} occurs in
both terms on the left:

{{{3x*red((x-3))+4*red((x-3))=0}}}

So factor out {{{red((x-3))}}}

{{{red((x-3))(3x+4)=0}}}

 x - 3 = 0      3x + 4 = 0
     x = 3          3x = -4
                     x ={{{-4/3}}}
Edwin</pre>