# Solution of equations using factoring - Examples, Exercises and Solutions

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 $0$.

## Practice Solution of equations using factoring

### Exercise #1

Find the value of the parameter x.

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

### Video Solution

$x=1,x=2.5$

### Exercise #2

Find the value of the parameter x.

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

### Video Solution

$x=-3,x=-4$

### Exercise #3

Find the value of the parameter x.

$(x-5)^2=0$

### Video Solution

$x=5$

### Exercise #4

Find the value of the parameter x.

$x^2-25=0$

### Video Solution

$x=5,x=-5$

### Exercise #5

Find the value of the parameter x.

$12x^3-9x^2-3x=0$

### Video Solution

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

### Exercise #1

Find the value of the parameter x.

$-2x(3-x)+(x-3)^2=9$

### Video Solution

$x=0,x=4$

### Exercise #2

Find the value of the parameter x.

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

### Video Solution

$x=0,x=10$

### Exercise #3

Find the value of the parameter x.

$(x+5)^2=0$

### Video Solution

$x=-5$

### Exercise #4

A right triangle is shown below.

x>1

Calculate the lengths of the sides of the triangle.

### Video Solution

$5,12,13$

### Exercise #5

A right triangle is shown below.

x>1

Find the lengths of the sides of the triangle.

### Video Solution

$6,8,10$

### Exercise #1

In front of you is a square.

The expressions listed next to the sides describe their length.

( x>-2 length measurements in cm).

Since the area of the square is 16.

Find the lengths of the sides of the square.

4

### Exercise #2

In front of you is a square.

The expressions listed next to the sides describe their length.

( x>-4 length measurements in cm).

Since the area of the square is 36.

Find the lengths of the sides of the square.

6

### Exercise #3

In front of you is an isosceles right triangle.

The expressions listed next to the sides describe their length.

( x>-5 length measurements in cm).

Since the area of the triangle is 12.5.

Find the lengths of the sides of the triangle.

### Video Solution

$5,5,5\sqrt{2}$

### Exercise #4

In front of you is an isosceles right triangle.

The expressions listed next to the sides describe their length.

( x>-8 length measurements in cm).

Since the area of the triangle is 32.

Find the lengths of the sides of the triangle.

### Video Solution

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