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