Solving a quadratic equation by factoring  Algebra II  Khan Academy  Summary and Q&A
TL;DR
Learn how to solve quadratic equations by factoring using the example of s^2  2s  35 = 0.
Questions & Answers
Q: What is the best way to solve quadratic equations?
The best way to solve quadratic equations, especially when it's explicitly equal to zero, is to factor the lefthand side and set each binomial equal to zero.
Q: How do you factor a quadratic equation by grouping?
To factor a quadratic equation by grouping, find two numbers whose sum is equal to the coefficient of the middle term and whose product is equal to the constant term. Split the middle term into two parts and factor out common factors from each group.
Q: What does it mean when the product of two numbers is equal to zero?
If the product of two numbers is equal to zero, it means that either one or both of the numbers must be equal to zero. This applies to the factored expressions in the quadratic equation as well.
Q: Is there a shortcut for factoring quadratic equations with a leading coefficient of 1?
Yes, when the leading coefficient is 1, you can directly factor the quadratic equation using the product of the two binomials where their sum is equal to the coefficient of the middle term and their product is equal to the constant term.
Summary & Key Takeaways

To solve a quadratic equation, factor the lefthand side and set each binomial equal to zero.

Use the method of factoring by grouping to split the middle term into two parts.

Factor out common factors from each group and solve for the values of s.