$x^3 + 3x^2 - 4x - 12 = 0$
$(x^3 + 3x^2) - (4x + 12) = 0$
$x^2(x + 3) - 4(x + 3) = 0$
$(x + 3)(x^2 - 4) = 0$
(x + 3)(x − 2)(x + 2) = 0
x + 3 = 0
$x_1 = -3$
x − 2 = 0
$x_2 = 2$
x + 2 = 0
$x_3 = -2$
Ответ:
$x_1 = -3$;
$x_2 = 2$;
$x_3 = -2$.

$2m^3 - m^2 - 18m + 9 = 0$
$(2m^3 - m^2) - (18m - 9) = 0$
$m^2(2m - 1) - 9(2m - 1) = 0$
$(2m - 1)(m^2 - 9) = 0$
(2m − 1)(m − 3)(m + 3) = 0
2m − 1 = 0
2m = 1
$m_1 = 0,5$
m − 3 = 0
$m_2 = 3$
m + 3 = 0
$m_3 = -3$
Ответ:
$m_1 = 0,5$;
$m_2 = 3$;
$m_3 = -3$.

$y^3 - 6y^2 = 6 - y$
$y^3 - 6y^2 - 6 + y = 0$
$(y^3 - 6y^2) + (y - 6) = 0$
$y^2(y - 6) + (y - 6) = 0$
$(y - 6)(y^2 + 1) = 0$
y − 6 = 0
y = 6
$y^2 + 1 = 0$
$y^2 = -1$ − решений нет.
Ответ: y = 6

$2a^3 + 3a^2 = 2a + 3$
$2a^3 + 3a^2 - 2a - 3 = 0$
$(2a^3 - 2a) + (3a^2 - 3) = 0$
$2a(a^2 - 1) + 3(a^2 - 1) = 0$
$(a^2 - 1)(2a + 3) = 0$
(a − 1)(a + 1)(2a + 3) = 0
a − 1 = 0
$a_1 = 1$
a + 1 = 0
$a_2 = -1$
2a + 3 = 0
2a = −3
$a_3 = -\frac{3}{2} = -1\frac{1}{2}$
Ответ:
$a_1 = 1$;
$a_2 = -1$;
$a_3 = -1\frac{1}{2}$.