How do you solve (x-3)(x+7)=0?

Apr 20, 2016

$x = 3 \textcolor{w h i t e}{\text{XX")orcolor(white)("XX}} x = - 7$

Explanation:

If $\left(a \times b\right) = 0$ then either $\left(a = 0\right)$ or $\left(b = 0\right)$

Based on this observation, we see that if $\left(x - 3\right) \left(x + 7\right) = 0$ then
either
$\textcolor{w h i t e}{\text{XXX")x-3=0color(white)("XX")rarrcolor(white)("XX}} x = 3$
or
$\textcolor{w h i t e}{\text{XXX")x+7=0color(white)("XX")rarrcolor(white)("XX}} x = - 7$

Apr 20, 2016

$x = \left\{- 7 , 3\right\}$

Explanation:

$\left(x - 3\right) \left(x + 7\right) = 0$

$\mathmr{if} \left(x - 3\right) = 0 \text{ " rArr" } x = 3$

$\mathmr{if} \left(x + 7\right) = 0 \text{ "rArr" } x = - 7$

$x = \left\{- 7 , 3\right\}$