Answer
$(-∞, -5/4]$ U $[3/2, ∞)$
Work Step by Step
$(2x-3)(4x+5) \geq 0$
$2x-3=0$
$2x-3+3=0+3$
$2x=3$
$2x/2=3/2$
$x=3/2$
$4x+5=0$
$4x+5-5=0-5$
$4x=-5$
$4x/4=-5/4$
$x=-5/4$
Three regions to test: $(-∞, -5/4]$, $[-5/4, 3/2]$, $[3/2, ∞)$
Let $x=-2$, $x=0$, $x=2$
$x=-2$
$(2x-3)(4x+5) \geq 0$
$(2*-2-3)(4*-2+5) \geq 0$
$(-4-3)(-8+5) \geq 0$
$(-7)(-3) \geq 0$
$21 \geq 0 $ (True)
$x=0$
$(2x-3)(4x+5) \geq 0$
$(2*0-3)(4*0+5) \geq 0$
$(0-3)(0+5) \geq 0$
$-3*5 \geq 0$
$-15 \geq 0$ (false)
$x=2$
$(2x-3)(4x+5) \geq 0$
$(2*2-3)(4*2+5) \geq 0$
$(4-3)(8+5) \geq 0$
$1*13 \geq 0$
$13 \geq 0$ (true)
