Find the value of the parameter x.$$ 12x^3-9x^2-3x=0 $$

$$ x=0,x=1,x=-\frac{1}{4} $$

$$ x=0,x=-1,x=\frac{1}{4} $$

$$ x=0,x=1,x=-\frac{1}{4} $$

$$ x=\frac{1}{4},x=1,x=-1 $$

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$$ 8,8,\frac{8}{\sqrt{2}} $$

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

Start practice

Test yourself on solution of equations using factoring!

Find the value of the parameter x.

$$ -x^2-7x-12=0 $$

Practice more now

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 $x=7$ .

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

At Tutorela you will find a variety of articles on mathematics.