1. The problem is to solve algebraic equations. 2. Algebraic equations are mathematical statements that assert the equality of two expressions. 3. The general approach to solving an equation is to isolate the variable on one side. 4. For example, consider the equation $ax + b = 0$ where $a \neq 0$. 5. To solve for $x$, subtract $b$ from both sides: $ax = -b$. 6. Then divide both sides by $a$: $x = \frac{-b}{a}$. 7. This method applies to linear equations. 8. For quadratic equations like $ax^2 + bx + c = 0$, use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 9. The discriminant $\Delta = b^2 - 4ac$ determines the nature of the roots. 10. If $\Delta > 0$, two real roots; if $\Delta = 0$, one real root; if $\Delta < 0$, complex roots. 11. Always check your solutions by substituting back into the original equation. 12. This process can be extended to higher degree polynomials and other algebraic expressions.