628. Решите уравнение: 1) (3x – 1)(x + 4) = −4; 2) (2x – 1)² – 6(6 – x) = 2x; 3) (x + 2)(x – 3) – (x – 5)(x + 5) = x² – x.

1. $$\begin{aligned} (3x - 1)(x + 4) &= -4 \\ 3x^2 + 12x - x - 4 &= -4 \\ 3x^2 + 11x &= 0 \\ x(3x + 11) &= 0 \\ x = 0 \quad \text{или} \quad 3x + 11 &= 0 \\ x = 0 \quad \text{или} \quad x &= -\frac{11}{3} \end{aligned}$$

2. $$\begin{aligned} (2x - 1)^2 - 6(6 - x) &= 2x \\ 4x^2 - 4x + 1 - 36 + 6x &= 2x \\ 4x^2 + 2x - 35 &= 2x \\ 4x^2 - 35 &= 0 \\ x^2 &= \frac{35}{4} \\ x &= \pm \sqrt{\frac{35}{4}} = \pm \frac{\sqrt{35}}{2} \end{aligned}$$

3. $$\begin{aligned} (x + 2)(x - 3) - (x - 5)(x + 5) &= x^2 - x \\ x^2 - 3x + 2x - 6 - (x^2 - 25) &= x^2 - x \\ x^2 - x - 6 - x^2 + 25 &= x^2 - x \\ -x + 19 &= x^2 - x \\ x^2 &= 19 \\ x &= \pm \sqrt{19} \end{aligned}$$

Ответ:

1. $$x = 0, x = -\frac{11}{3}$$
2. $$x = \pm \frac{\sqrt{35}}{2}$$
3. $$x = \pm \sqrt{19}$$