Solve the inequality
a^2(a-4)(a+3)>0

Answer is in the file below

cutt.ly/rzNrBcz

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

this may not be at all, but i use the same website you're using for school, and if i'm stuck doing one of these i try to look for it on the section.