1) -x(-2x+1)-2x2=5
\(\Leftrightarrow\) 2x2-x-2x2=5
\(\Leftrightarrow\) -x=5
\(\Leftrightarrow\) x= -5
2) 2x(-x-\(\dfrac{1}{2}\))+2x2=2
\(\Leftrightarrow\) -2x2 - xx + 2x2 = 2
\(\Leftrightarrow\) -x = 2
\(\Leftrightarrow\) x = -2
3) -3x(-4x-1)+6x(4-2x)=0
\(\Leftrightarrow\) 12x2 + 3x + 24x - 12x2 = 0
\(\Leftrightarrow\) 27x = 0
\(\Leftrightarrow\) x = 0
4) 5x(-x+1) - 5(-x2-x)=0
\(\Leftrightarrow\) -5x2 + 5x + 5x2 + 5x = 0
\(\Leftrightarrow\) 10x = 0
\(\Leftrightarrow\) x = 0
5) -\(\dfrac{7}{3}\)x(3x+1) - \(\dfrac{1}{2}\)x(2-14x)=0
\(\Leftrightarrow\) -7x2 - \(\dfrac{7}{3}\)x - \(\dfrac{1}{2}\)x.2(1-7x) = 0
\(\Leftrightarrow\) -7x2 - \(\dfrac{7}{3}\)x - x.(1-7x) = 0
\(\Leftrightarrow\) -7x2 - \(\dfrac{7}{3}\)x - x + 7x2 = 0
\(\Leftrightarrow\) - \(\dfrac{7}{3}\)x - x = 0
\(\Leftrightarrow\) -7x - 3x = 0
\(\Leftrightarrow\) -10x = 0
\(\Leftrightarrow\) x = 0
6) -10x(2-x) - 5x(x+2) = 5x(x+3)
\(\Leftrightarrow\) -20x + 10x2 - 5x2 -10xx = 5x2 + 15x
\(\Leftrightarrow\) -30x + 5x2 = 5x2 +15x
\(\Leftrightarrow\) -30x = 15x
\(\Leftrightarrow\) -30x - 15x = 0
\(\Leftrightarrow\) -45x = 0
\(\Leftrightarrow\) x = 0
7) x(5-2x) + 2x(x-1) = 15
\(\Leftrightarrow\) 5x - 2x2 + 2x2 -2x = 15
\(\Leftrightarrow\) 3x = 15
\(\Leftrightarrow\) x = 5
8) 5x - 3\(\left\{4x-2\left[4x-3\left(5x-2\right)\right]\right\}\) = 182
\(\Leftrightarrow\) 5x - 3 \(\left[4x-2\left(4x-15x+6\right)\right]\) = 182
\(\Leftrightarrow\) 5x - 3 \(\left[4x-2\left(-11+6\right)\right]\) = 182
\(\Leftrightarrow\) 5x - 3 (4x + 22x - 12) = 182
⇔ 5x - 3(26x - 12) = 182
⇔ 5x - 78x + 36 = 182
⇔ -73x + 36 = 182
⇔ -73x = 182 - 36
⇔ -73x = 146
⇔ x=-2