Consider the quadratic equation 6x2+9x−15=0.
(i) Divide the entire equation by the highest common factor of all three terms and rewrite it in simpler form.
(ii) Factorise the simplified quadratic expression completely.
(iii) Hence, determine both values of x that satisfy the original equation.
(iv) Check your answers by direct substitution in 6x2+9x−15=0.