How would you write the equation 2x(2-x-4(x-2))=(3x-4)(4x-3) in standard form ax^2+bx+c=0

Distribute first:

2x(2-x-4x+8)=12x^2 -9x-16x+12

Then Add Like Terms:

2x(10-5x)=12x^2-25x+12

Distribute again:

20x-10x^2 = 12x^2-25x+12

Subtract, Add, Divide, and Multiply each side as necessary:

45x = 22x^2 +12

>> 22x^2 - 45x +12 = 0
or ax^2+bx+c

where a= 22
b= -45
c= 12

Voila!!!!

2x(2 - x - 4(x - 2)) = (3x - 4)(4x - 3)
2x(2 - x - 4x + 8) = 12x^2 - 9x - 16x +12
2x(10 - 5x) = 12x^2 - 25x +12
20x - 10x^2 = 12x^2 - 25x + 12
0 = 12x^2 + 10x^2 - 25x - 20x + 12
0 = 22x^2 - 45x + 12

In order:
Distributive property and FOIL method.
Combine like terms.
Distributive property.
Move everything to the same side.
Combine like terms.

Oh, and if you multiply the whole thing by -1, you get the equally valid:
0 = - 22x^2 + 45x - 12

The main thing to remember is that, when working with nested parentheses (parentheses inside parentheses), you need to work on the innermost parentheses first.

Oh, and I totally glanced over FOIL. If you don't know, FOIL is a mnemonic to remember how to multiply two binomials. It stands for First, Outer, Inner Last.

Using foil, if you had (a + b)(c + d):
(a + b)(c + d)
ac + ad + bc + bd

Work the left side from the inside out:

2x(2 - x - 4(x-2)) = 2x(2 - x - 4x + 8)

Simplify:

2x(2 - x - 4x + 8) = 2x(-5x + 10)

Multiply out:

2x(-5x + 10) = -10x^2 + 20x


Multiply out the right side using FOIL:

(3x - 4)(4x - 3) = 12x^2 - 25x + 12


Combine into:

-10x^2 + 20x = 12x^2 - 25x + 12

Add 10x^2 to both sides and flip it around:

22x^2 - 25x + 12 = 20x

Subtract 20x from both sides:

22x^2 - 45x + 12 = 0