Here's a breakdown of the steps:
1. Arrange the equation in standard form:
Make sure the equation is written in the form ax^2 + bx + c = 0
, where a, b, and c are coefficients (numbers), and x is the unknown variable.
2. Find two numbers that multiply to ac and add up to b:

Identify the coefficients a, b, and c from the equation.

Find two numbers that:

Multiply together to equal
a x c
(the product of the first and last term's coefficients).

Add up to equal
b
(the coefficient of the middle term).
3. Rewrite the middle term using those two numbers:
Replace the middle term (bx
) with the sum of the two numbers you just found multiplied by each other.
4. Factor by grouping:
Group the terms so that there's a common factor in each group. Then, factor out the common factors.
5. Simplify the expression:
Combine like terms and write the equation in its factored form.
There are also some special cases where you can use factoring by perfect squares or the sumproduct pattern to simplify the process.
If you'd like to see some examples or need help working through a specific quadratic equation, feel free to ask!