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There are a couple of ways to factor quadratic equations, but the most common method involves finding two specific numbers.

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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 sum-product 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!

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