Đáp án:

Bài 1)
$7) {\left[\begin{aligned}x=\dfrac{15}{2}\\3-x=0\end{aligned}\right.}\\
8) {\left[\begin{aligned}x=0\\x=2\end{aligned}\right.}\\
10)
x=6$
Bài 2)
$8)  {\left[\begin{aligned}x=-\dfrac{1}{2}\\x=\dfrac{1}{3}\end{aligned}\right.}\\
9)
 {\left[\begin{aligned}x=0\\x=\dfrac{4}{3}\end{aligned}\right.}\\
10)
x=\dfrac{-1}{2}\\
11)
 x=\dfrac{-23}{2}\\
12)
 {\left[\begin{aligned}x=5\\x=-3\end{aligned}\right.}\\
13)
 x=\pm \dfrac{\sqrt{15}}{4}\\
14)
 x=\dfrac{-1}{2}\\
15)
 {\left[\begin{aligned}x=\dfrac{13}{10}\\x=-\dfrac{3}{10}\end{aligned}\right.}\\$

Giải thích các bước giải:

 Bài 1)
$7) (2x-15)(3-x)=0\\
\Leftrightarrow {\left[\begin{aligned}2x-15=0\\3-x=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}2x=15\\x=3\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{15}{2}\\3-x=0\end{aligned}\right.}\\
8) x(x-5)+3x=0\\
\Leftrightarrow x^2-5x+3x=0\\
\Leftrightarrow x^2-2x=0\\
\Leftrightarrow x(x-2)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x-2=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=2\end{aligned}\right.}\\
10)
12+(3-x)^3=-15\\
\Leftrightarrow (3-x)^3=-15-12=-27\\
\Leftrightarrow 3-x=-3\\
\Leftrightarrow x=3+3=6$
Bài 2)
$8) \left ( x+\dfrac{1}{2} \right ).\left ( \dfrac{2}{3}-2x \right )=0\\
\Leftrightarrow {\left[\begin{aligned}x+\dfrac{1}{2}=0\\\dfrac{2}{3}-2x=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=-\dfrac{1}{2}\\2x=\dfrac{2}{3}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=-\dfrac{1}{2}\\x=\dfrac{1}{3}\end{aligned}\right.}\\
9)
2x.\left ( x+\dfrac{2}{3} \right )-4x=0\\
\Leftrightarrow 2x.\left ( x+\dfrac{2}{3} \right )-4x=0\\
\Leftrightarrow 2x^2+\dfrac{4}{3}x-4x=0\\
\Leftrightarrow 2x^2-\dfrac{8}{3}x=0\\
\Leftrightarrow 2x\left ( x-\dfrac{4}{3} \right )=0\\
\Leftrightarrow {\left[\begin{aligned}2x=0\\x-\dfrac{4}{3}=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=\dfrac{4}{3}\end{aligned}\right.}\\
10)
\dfrac{2}{3}x-\dfrac{3}{2}x=\dfrac{5}{12}\\
\Leftrightarrow \dfrac{4}{6}x-\dfrac{9}{6}x=\dfrac{5}{12}\\
\Leftrightarrow \dfrac{-5}{6}x=\dfrac{5}{12}\\
\Leftrightarrow x=\dfrac{5}{12}.\dfrac{-6}{5}=\dfrac{-1}{2}\\
11)
\dfrac{x-5}{3}=\dfrac{2x+1}{4}\\
\Leftrightarrow 4(x-5)=3(2x+1)\\
\Leftrightarrow 4x-20=6x+3\\
\Leftrightarrow 4x-6x=3+20\\
\Leftrightarrow -2x=23\\
\Leftrightarrow x=\dfrac{-23}{2}\\
12)
\dfrac{x-1}{-2}=\dfrac{-8}{x-1}\\
\Leftrightarrow (x-1)^2=16\\
\Leftrightarrow x-1=\pm 4\\
\Leftrightarrow {\left[\begin{aligned}x-1=4\\x-1=-4\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=5\\x=-3\end{aligned}\right.}\\
13)
1-x^2=\dfrac{15}{16}\\
\Leftrightarrow x^2=1-\dfrac{15}{16}\\
\Leftrightarrow x^2=\dfrac{16}{16}-\dfrac{15}{16}\\
\Leftrightarrow x^2=\dfrac{1}{16}\\
\Leftrightarrow x=\pm \dfrac{\sqrt{15}}{4}\\
14)
-2x^3+3=\dfrac{13}{4}\\
\Leftrightarrow -2x^3=\dfrac{13}{4}-3=\dfrac{13}{4}-\dfrac{3.4}{4}\\
\Leftrightarrow -2x^3=\dfrac{1}{4}\\
\Leftrightarrow x^3=\dfrac{-1}{8}\\
\Leftrightarrow x=\dfrac{-1}{2}\\
15)
\left ( x-\dfrac{1}{2} \right )^2=\dfrac{16}{25}\\
\Leftrightarrow x-\dfrac{1}{2}=\pm \dfrac{4}{5}\\
\Leftrightarrow {\left[\begin{aligned}x-\dfrac{1}{2}=\dfrac{4}{5}\\x-\dfrac{1}{2}=-\dfrac{4}{5}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{4}{5}+\dfrac{1}{2}\\x=-\dfrac{4}{5}+\dfrac{1}{2}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{4.2}{10}+\dfrac{5}{10}\\x=-\dfrac{8}{10}+\dfrac{5}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{13}{10}\\x=-\dfrac{3}{10}\end{aligned}\right.}\\$