Example

Solve for $y$: $\quad (y^2-11)^2-10(y^2-11)+25=0$

Solution

The substitution $u=y^2-11$ transforms the equation to quadratic:

The new equation can be solved by factoring:

The quadratic equation has the single solution $u=5$, but we are interested in the solutions for the variable $y$. To find those, we must resubstitute and resolve.

The original equation has two solutions: $y=-4$ or $y=4$.