Let's calculate each equation step by step:

(7x + 1)(3x - 1) - 21x^2
Expand the terms inside the parentheses:
= 21x^2 - 7x + 3x - 1 - 21x^2
Combine like terms:
= -4x - 1

(1 - 4x)(1 - 3x)
Expand the terms inside the parentheses:
= 1 - 3x - 4x + 12x^2
Combine like terms:
= 12x^2 - 7x + 1

6x(2x - 1)
Distribute the 6x:
= 12x^2 - 6x

Therefore, the equations in simplified form are:

(7x + 1)(3x - 1) - 21x^2 = -4x - 1(1 - 4x)(1 - 3x) = 12x^2 - 7x + 16x(2x - 1) = 12x^2 - 6x