You are given 12x2−7x−10=0 to factorise.

• The first step is to find two numbers which
  • add to give -7
  • and multiply to give a×c where a=12 and c=−10; 12×−10=−120.
• These are −15 and 8.
• Splitting the middle term gives us  12x2−15x+8x−10=0.
• Factorising each pair gives us 3x(4x−5)+2(4x−5)=0
• Which finally factorises to (3x+2)(4x−5)=0

Once you've factorised it, you need to find the roots.

As the equation consists of two factors which multiply together to make 0, one of the factors must equal 0, so we have

3x+2=0

or

4x−5=0

The first equation gives us x=−23, and the second x=54.