1. The problem is to solve an equation using substitution method. 2. Substitution involves replacing a complicated expression with a simpler variable to make the equation easier to solve. 3. For example, if the equation is $x^4 - 5x^2 + 6 = 0$, let $u = x^2$. 4. Then the equation becomes $u^2 - 5u + 6 = 0$. 5. Solve the quadratic equation $u^2 - 5u + 6 = 0$ using factoring: $$u^2 - 5u + 6 = (u - 2)(u - 3) = 0$$ 6. So, $u = 2$ or $u = 3$. 7. Substitute back $u = x^2$: $$x^2 = 2 \quad \text{or} \quad x^2 = 3$$ 8. Solve for $x$: $$x = \pm \sqrt{2} \quad \text{or} \quad x = \pm \sqrt{3}$$ 9. The solutions are $x = \pm \sqrt{2}$ and $x = \pm \sqrt{3}$. This method simplifies solving higher degree polynomials by substitution.