Solving quadratic equations by factoring could be many times the simplest and quickest way to solve quadratic equation as long as you know how to factor.

I strongly recommend you to study or review the following important unit: Factoring

Solve x

First, you have to factor x

Since the coefficient of x

2 = 1 × 2

2 = -1 × -2

Since 1 + 2 = 3, and 3 is the coefficient of the second term, x

x

( x + 2) × ( x + 1) = 0

( x + 2) × ( x + 1) = 0 when either x + 2 = 0 or x + 1 = 0

x + 2 = 0 when x = -2

x + 1 = 0 when x = -1

Let us now check x = -2 and x = -1 are indeed solutions of x

(-2)

(-1)

If instead you were solving x

x

( x + -2) × ( x + -1) = 0

( x + -2) × ( x + -1) = 0 when either x + -2 = 0 or x + -1 = 0

x + -2 = 0 when x = 2

x + -1 = 0 when x = 1

Check that this are indeed the solutions

Solve x

First, you have to factor x

-30 = 30 × -1

-30 = 15 × -2

-30 = 6 × -5

-30 = -30 × 1

-30 = -15 × 2

-30 = -6 × 5

Since only 6 + -5 = 1, and 1 is the coefficient of the second term(x =

x

( x + 6) × ( x - 5) = 0

( x + 6) × ( x - 5) = 0 when either x + 6 = 0 or x - 5 = 0

x + 6 = 0 when x = -6

x - 5 = 0 when x = 5

Let us now check x = -6 and x = 5 are indeed solutions of x

(-6)

(5)

If instead you were solving x

x

( x - 6) × ( x + 5) = 0

( x - 6) × ( x + 5) = 0 when either x - 6 = 0 or x + 5 = 0

x - 6 = 0 when x = 6

x + 5 = 0 when x = -5

Check that this are indeed the solutions

Solving quadratic equations by factoring can get very tough. See below:

6x

First factor 6x

6x

Now, factor the last term 30

30 = 30 × 1

30 = 15 × 2

30 = 6 × 5

To get the 27x, you have to try out the cross multiplications below. There are 6 of them.

6x x

30 1

6x + 30x = 36x

15 2

12x + 15x = 27x

6 5

30x + 6x = 36x

3x 2x

30 1

3x + 60x = 63x

3x 2x

15 2

6x + 30x = 36x

6 5

15x + 12x = 27x

6x

(6x + 15) × ( x + 2)= 0

6x + 15 = 0

6x = -15

x = -15/6

x + 2 = 0

x = -2