# The product of three more than a number times two less than the number is fourteen. How do you find the number?

Nov 18, 2016

The number is either $- 5$ or $4$.

#### Explanation:

From the given data, we can write the equation:

$\left(x + 3\right) \times \left(x - 2\right) = 14$

Opening the brackets and simplifying, we get:

${x}^{2} + 3 x - 2 x - 6 = 14$

${x}^{2} + x - 6 = 14$

Subtract $14$ from each side.

${x}^{2} + x - 20 = 0$

Factorise.

${x}^{2} + 5 x - 4 x - 20 = 0$

$x \left(x + 5\right) - 4 \left(x + 5\right) = 0$

$\left(x + 5\right) \left(x - 4\right) = 0$

$x + 5 = 0$ or $x - 4 = 0$

$x = - 5$ or $x = 4$