Solving Equations by Factoring

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

Let's remember the following property

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

Steps to carry out to solve equations through factorization

Let's move all the elements to one side of the equation and leave $0$ 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 $0$ .

Detailed explanation

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Test yourself on solution of equations using factoring!

Find the value of the parameter x.

$$ (x-5)^2=0 $$

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Example to solve equations through factorization
$x^2+49=14x$
First, we will transpose all the terms to one side of the equation. On the other side, we will leave $0$ .
We will obtain:
$x^2+49-14x=0$
We see that it is a trinomial. Let's arrange the equation to clearly see the trinomial:
$x^2-14x+49=0$
Now, let's factorize and we will obtain:
$(x-7)(x-7)=0$
We can easily realize that the equation equals zero when $x=7$
Therefore, the solution to the exercise is $x=7$ .