Factorise the quadratic as . So the equation becomes .

The quadratic function has a minimum value –1/4 (when t=2.5). So the equation f(t) = c has two solutions if c>–1/4, one solution if c=–1/4, and no solutions if c<–1/4. If t=|x| (and t>0), then , so there will be two values of x for each value of t.

Now put that information together to find one value of k for which the equation has six solutions.