Solving Equations by Factoring

🏆Practice solution of equations using factoring

To solve equations through factorization, we must transpose all the elements to one side of the equation and leave 0 0 on the other side.
Why? Because after factoring, we will have 0 0 as the product.

Let's remember the following property

The product of two numbers equals 0 0 when, at least, one of them is 0 0 .
If  x×y=0x\times y=0
either: x=0x=0
or: y=0y=0
or both are equal to 0 0 .

Steps to carry out to solve equations through factorization

  • Let's move all the elements to one side of the equation and leave 0 0 on the other.
  • Let's factor using one of the methods we have learned: by taking out the common factor, with shortcut multiplication formulas, or with trinomials.
  • Let's find out when the elements achieve a product equivalent to 0 0 .
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Test yourself on solution of equations using factoring!


Find the value of the parameter x.

\( -x^2-7x-12=0 \)

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Example to solve equations through factorization
First, we will transpose all the terms to one side of the equation. On the other side, we will leave 0 0 .
We will obtain:
We see that it is a trinomial. Let's arrange the equation to clearly see the trinomial:
Now, let's factorize and we will obtain:
We can easily realize that the equation equals zero when x=7x=7
Therefore, the solution to the exercise is x=7x=7.

If you are interested in this article, you might also be interested in the following articles:

  • The uses of factorization
  • Factorization according to short multiplication formulas
  • Factorization through the extraction of the common factor outside the parentheses
  • Factorization of trinomials
  • Factorization of algebraic fractions
  • Addition and subtraction of algebraic fractions
  • Simplification of algebraic fractions
  • Multiplication and division of algebraic fractions

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