$(a + 1)^2 - (2a + 3)^2 = 0$
(a + 1 − (2a + 3))(a + 1 + 2a + 3) = 0
(a + 1 − 2a − 3)(3a + 4) = 0
(−a − 2)(3a + 4) = 0
−a − 2 = 0
−a = 2
a = −2
или
3a + 4 = 0
3a = −4
$a = -\frac{4}{3} = -1\frac{1}{3}$
Ответ: $-2; -1\frac{1}{3}$.

$(5c + 8)^2 - (c - 10)^2 = 0$
(5c + 8 − (c − 10))(5c + 8 + c − 10) = 0
(5c + 8 − c + 10)(6c − 2) = 0
(4c + 18)(6c − 2) = 0
4c + 18 = 0
4c = −18
$c = -\frac{18}{4} = -\frac{9}{2} = -4\frac{1}{2}$
или
6c − 2 = 0
6c = 2
$c = \frac{2}{6} = \frac{1}{3}$
Ответ: $-4\frac{1}{2}; \frac{1}{3}$.

$(3b - 2)^2 - (b + 1)^2 = 0$
(3b − 2 − (b + 1))(3b − 2 + b + 1) = 0
(3b − 2 − b − 1)(4b − 1) = 0
(2b − 3)(4b − 1) = 0
2b − 3 = 0
2b = 3
$b = \frac{3}{2} = 1\frac{1}{2}$
или
4b − 1 = 0
4b = 1
$b = \frac{1}{4}$
Ответ: $\frac{1}{4}; 1\frac{1}{2}$.

$(7d - 13)^2 - (9d - 25)^2 = 0$
(7d − 13 − (9d − 25))(7d − 13 + 9d − 25) = 0
(7d − 13 − 9d + 25)(16d − 38) = 0
(12 − 2d)(16d − 38) = 0
12 − 2d = 0
−2d = −12
d = 6
или
16d − 38 = 0
16d = 38
$d = \frac{38}{16} = \frac{19}{8} = 2\frac{3}{8}$
Ответ: $2\frac{3}{8}; 6$.