Solving quadratic equations by factorizing
Question
$\displaystyle \frac{25}{6}x^2=\frac{8}{3} $
Attempt
$\displaystyle 75x^2-48=0 $
Immediately the 6 and the 3 can be cancelled to 2 and 1 respectively:
$\displaystyle \frac{25}{2}x^2 = 8$
Take 8 from both sides:
$\displaystyle \frac{25}{2}x^2 - 8 =0$
Multiply through by 2 to clear the denominator:
$\displaystyle 25x^2 -16 = 0$
Now you can use the difference of two squares to factorise