# The product of some negative number and 7 less than three times that number is 6. How do you find the number?

Dec 11, 2016

The number is $- 3$.

#### Explanation:

Let us consider the negative number as $- x$. From the data, we can write:

$- x \left(- 3 x - 7\right) = 6$

Open the brackets.

$3 {x}^{2} + 7 x = 6$

Subtract $6$ from both sides.

$3 {x}^{2} + 7 x - 6 = 0$

Factorise.

$3 {x}^{2} + 9 x - 2 x - 6 = 0$

$3 x \left(x + 3\right) - 2 \left(x + 3\right) = 0$

$\left(3 x - 2\right) \left(x + 3\right) = 0$

$3 x - 2 = 0$ or $x + 3 = 0$

$3 x = 2$ or $x = - 3$

$x = \frac{2}{3}$ or $x = - 3$

Applying the given data to the two possibilities, only the second possibility applies.

$\therefore x = - 3$