Hi
Your question would be better with " Could you help me please ? " at the end. Quite sure your mum told you that some time in the past.
I will show you how to solve but you will do the calculus. Math is all about rules, methods and training. If you dont practice, you will never progress.
rule : you must know by heart your remarkable identities.
Here we have : ( 4x-3)² - (2x+5)² = 0
It 's of the form A² -B² = ( A+B) ( A-B)
here A is : 4x-3 and B is 2x+5
Now let's apply rule : ( 4x-3)² - (2x+5)² = ( (4x-3) +( 2x+5) ) ( (4x-3) - (2x+5)
= ( 4x-3 +2x+5 ) ( 4x-3 -2x-5 )
= ( 6x +2) ( 2x-8)
so : ( 4x-3)² - (2x+5)² = ( 6x +2) ( 2x-8)
so ( 4x-3)² - (2x+5)² = 0 means : ( 6x +2) ( 2x-8) = 0
Rule A*B = 0 if A = 0 or B = 0
A is 6x+2 and B = 2x-8
So I let you now work :
You have to solve : 6x+2 = 0
and 2x-8 = 0
Solutions of this two calculus will be the solutions of ( 4x-3)² - (2x+5)² = 0
Have fun !