The equations in mathematics are open sentences that have truth, right or wrong values. For example linear equations one variable: $2x-1=3$, linear equations two variables: $x+2y=4$, quadratic equations: $x^2+5x+6=0$, and others.

## Two solutions were found :

- x = -2
- x = -3

## Step by step solution :

## Step 1 :

#### Trying to factor by splitting the middle term

^{2}+5x+6

The first term is, x^{2} its coefficient is 1 .

The middle term is, +5x its coefficient is 5 .

The last term, “the constant”, is +6

Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is 5 .

-6 | + | -1 | = | -7 | ||

-3 | + | -2 | = | -5 | ||

-2 | + | -3 | = | -5 | ||

-1 | + | -6 | = | -7 | ||

1 | + | 6 | = | 7 | ||

2 | + | 3 | = | 5 | That’s it |

x

^{2}+ 2x + 3x + 6

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+2)

Add up the last 2 terms, pulling out common factors :

3 • (x+2)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x+2)

Which is the desired factorization

#### Equation at the end of step 1 :

` (x + 3) • (x + 2) = 0 `

## Step 2 :

#### Theory – Roots of a product :

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

#### Solving a Single Variable Equation :

#### Solving a Single Variable Equation :

### Supplement : Solving Quadratic Equation Directly

`Solving x`^{2}+5x+6 = 0 directly

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