$(2x - 3)(4x + 3) - 8x^2 = 33$
$8x^2 - 12x + 6x - 9 - 8x^2 = 33$
−12x + 6x = 33 + 9
−6x = 42
x = 42 : −6
x = −7

(2x − 6)(8x + 5) + (3 − 4x)(3 + 4x) = 55
$16x^2 - 48x + 10x - 30 + 9 - 12x + 12x - 16x^2 = 55$
−48x + 10x = 55 + 30 − 9
−38x = 76
x = 76 : −38
x = −2

$21x^2 - (3x - 7)(7x - 3) = 37$
$21x^2 - (21x^2 - 49x - 9x + 21) = 37$
$21x^2 - 21x^2 + 49x + 9x - 21 = 37$
49x + 9x = 37 + 21
58x = 58
x = 58 : 58
x = 1

(x + 1)(x + 2) − (x − 3)(x + 4) = 12
$x^2 + x + 2x + 2 - (x^2 - 3x + 4x - 12) = 12$
$x^2 + x + 2x + 2 - x^2 + 3x - 4x + 12 = 12$
x + 2x + 3x − 4x = 12 − 12 − 2
2x = −2
x = −2 : 2
x = −1

(−4x + 1)(x − 1) − x = (5 − 2x)(2x + 3) − 17
$-4x^2 + x + 4x - 1 - x = 10x - 4x^2 + 15 - 6x - 17$
$-4x^2 + 4x^2 + x + 4x - x - 10x + 6x = 1 + 15 - 17$
0 ≠ −1, уравнение не имеет корней.