What is x if -4(x+2)^2+3x=-5?

Jan 11, 2016

$x = - \frac{9}{4}$ or $x = - 1$

Explanation:

First expand the expression and move the $- 5$ to the left hand side, to get it into standard form
$- 4 \left({x}^{2} + 4 x + 4\right) + 3 x + 5 = 0$
$- 4 {x}^{2} - 16 x - 16 + 3 x + 5 = 0$
$- 4 {x}^{2} - 13 x - 9 = 0$
$- \left(4 {x}^{2} + 13 x + 9\right) = 0$
$4$ and $9$ add to give $13$, so the factors we need are 4&1 and 9&1
$- \left(4 x + 9\right) \left(x + 1\right) = 0$
$\therefore x = - \frac{9}{4}$ or $x = - 1$