# How do you solve -5x^2 + 10x + 15 = 0?

Jun 18, 2016

$x = - 1 \mathmr{and} x = 3$

#### Explanation:

$- 5 {x}^{2} + 10 x + 15 = 0$
$= - 5 \left({x}^{2} - 2 x - 3\right) = 0$
To factorize the polynomial ${x}^{2} - 2 x - 3$ in the form $\left(x + a\right) \left(x + b\right)$
we have to find two integers $a$ and $b$ such that
$a + b = - 2$ and $a \cdot b = - 3$

check for $a = 1$ and $b = - 3$
so,$\textcolor{b l u e}{\left({x}^{2} - 2 x - 3\right) = \left(x + 1\right) \left(x - 3\right)}$

$- 5 {x}^{2} + 10 x + 15 = 0$
$\Rightarrow - 5 \left(x + 1\right) \left(x - 3\right) = 0$

Knowing that if the product is zero then one of the factors can be equal to zero .

Since $- 5 \ne 0$
Therefore,

$x + 1 = 0$
$x = - 1$

Or,
$x - 3 = 0$
$x = 3$