a) \(3x\left(x+1\right)-\left(x-2\right)\left(3x+1\right)=12\)
\(\Leftrightarrow3x^2+3x-3x^2+5x+2=12\)
\(\Leftrightarrow8x=10\Leftrightarrow x=\dfrac{5}{4}\)
b) \(\left(3x^2-x+1\right)\left(x-1\right)+x^2\left(4-3x\right)=\dfrac{5}{2}\)
\(\Leftrightarrow3x^3-3x^2-x^2+x+x-1+4x^2-3x^3=\dfrac{5}{2}\)
\(\Leftrightarrow2x=\dfrac{7}{2}\Leftrightarrow x=\dfrac{7}{4}\)
c) \(\left(x+3\right)\left(5x-1\right)=5\left(x+1\right)\left(x-2\right)\)
\(\Leftrightarrow5x^2+14x-3=5x^2-5x-10\)
\(\Leftrightarrow19x=-7\Leftrightarrow x=-\dfrac{7}{19}\)
d) \(\left(2x-3\right)\left(x+1\right)=2x\left(x-1\right)\)
\(\Leftrightarrow2x^2-x-3=2x^2-2x\)
\(\Leftrightarrow x=3\)
e) \(\dfrac{1}{4}x^2-\left(\dfrac{1}{2}x-4\right)\dfrac{1}{2}x=-14\)
\(\Leftrightarrow\dfrac{1}{4}x^2-\dfrac{1}{4}x^2+2x=-14\)
\(\Leftrightarrow2x=-14\Leftrightarrow x=-7\)
f) \(3\left(1-4x\right)\left(x-1\right)+4\left(3x-2\right)\left(x+3\right)=-27\)
\(\Leftrightarrow-12x^2+15x-3+12x^2+28x-24=-27\)
\(\Leftrightarrow43x=0\Leftrightarrow x=0\)
a) 3x(x-1)-(x-2)(3x+1)=12
3x^2-3x-(3x^2+x-6x-x-2)=12
3x^2-3x-3x^2-x+6x+x-2=12
2x =14
x =7
b) (3x^2-x+1)(x-1)+x^2(4-3x)=5/2
3x^2-3x^2-x^2+x+x-1+4x^2-3x^3=5/2
2x-1 =5/2
2x =7/2
x =7/4
