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 $0$ 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 $0$.

Test yourself on solution of equations using factoring!

Find the value of the parameter x.

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

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 $x=7$.

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Examples and exercises with solutions for solving equations through factorization

Exercise #1

Find the value of the parameter x.

$(x-4)^2+x(x-12)=16$

Step-by-Step Solution

Let's open parentheses, remembering that there might be more than one solution for the value of X:

$(x-4)^2+x(x-12)=16$

$x^2-8x+16+x^2-12x=16$

$2x^2-20x=0$

$2x(x-10)=0$

Therefore:

$x-10=0$

$x=10$

Or:

$2x=0$

$x=0$

$x=0,x=10$

Exercise #2

Find the value of the parameter x.

$(x-5)^2=0$

Video Solution

$x=5$

Exercise #3

Find the value of the parameter x.

$x^2-25=0$

Video Solution

$x=5,x=-5$

Exercise #4

Find the value of the parameter x.

$2x^2-7x+5=0$

Video Solution

$x=1,x=2.5$

Exercise #5

Find the value of the parameter x.

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

Video Solution

$x=-3,x=-4$