First I will start from third equation
X^2+12X-64=0
X^2+X(16-4)-(16*4)=0
X^2+16X-4X-(16*4)=0
Now we will take common
X(X+16) -4(X+16)=0
(X+16)(X-4)=0
X=-16 and X=4 {you can check this... By solving this (X+16)(X-4) = X^2+12X-64}
Now the forth equation
2X^2-3X-5=0
now we will break the middle term
2X^2-(5-2)X-5=0
2X^2 -5X + 2X - 5 = 0
2X^2+2X-5X-5=0
Now we will take common
2X(X+1) - 5(X+1) = 0
(2X-5)(X+1) = 0
2X-5 = 0 , X+1=0
X=5/2 and X=-1
Now second equation
4X^2-4X+3 = 0
4X^2-(6-2)X+3 = 0
4X^2-6x+2X+3 = 0
4X^2+2X-6X+3=0
2X(2X+1) -3(2X+1)=0
(2X-3)(2X+1)=0
I am not able to understand your first equation
Hope this helps
Gud luck
X^2+12X-64=0
X^2+X(16-4)-(16*4)=0
X^2+16X-4X-(16*4)=0
Now we will take common
X(X+16) -4(X+16)=0
(X+16)(X-4)=0
X=-16 and X=4 {you can check this... By solving this (X+16)(X-4) = X^2+12X-64}
Now the forth equation
2X^2-3X-5=0
now we will break the middle term
2X^2-(5-2)X-5=0
2X^2 -5X + 2X - 5 = 0
2X^2+2X-5X-5=0
Now we will take common
2X(X+1) - 5(X+1) = 0
(2X-5)(X+1) = 0
2X-5 = 0 , X+1=0
X=5/2 and X=-1
Now second equation
4X^2-4X+3 = 0
4X^2-(6-2)X+3 = 0
4X^2-6x+2X+3 = 0
4X^2+2X-6X+3=0
2X(2X+1) -3(2X+1)=0
(2X-3)(2X+1)=0
I am not able to understand your first equation
Hope this helps
Gud luck