a: \(\left(3x-1\right)\left(2x+7\right)-\left(x+1\right)\left(6x-5\right)=16\)
=>\(6x^2+21x-2x-7-\left(6x^2-5x+6x-5\right)=16\)
=>\(6x^2+19x-7-6x^2-x+5=16\)
=>18x-2=16
=>18x=18
=>x=1
b: \(x\left(x+1\right)\left(x+6\right)-x^3=5x\)
=>\(x\left(x^2+7x+6\right)-x^3-5x=0\)
=>\(x^3+7x^2+6x-x^3-5x=0\)
=>\(7x^2+x=0\)
=>x(7x+1)=0
=>\(\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{7}\end{matrix}\right.\)
c: \(\left(10x+9\right)\cdot x-\left(5x-1\right)\left(2x+3\right)=8\)
=>\(10x^2+9x-\left(10x^2+15x-2x-3\right)=8\)
=>\(10x^2+9x-10x^2-13x+3=8\)
=>-4x+3=8
=>-4x=7
=>\(x=-\dfrac{7}{4}\)
d: \(\left(3x-5\right)\left(-5x+7\right)-\left(5x+2\right)\left(-3x+2\right)=4\)
=>\(-15x^2+21x+25x-35-\left(-15x^2+10x-6x+4\right)=4\)
=>\(-15x^2+46x-35+15x^2-4x-4=4\)
=>42x-39=4
=>42x=43
=>\(x=\dfrac{43}{42}\)
e: \(\left(3x-5\right)\left(7-5x\right)+\left(5x+2\right)\left(3x-2\right)-2=0\)
=>\(21x-15x^2-35+25x+15x^2-10x+6x-4-2=0\)
=>42x-41=0
=>\(x=\dfrac{41}{42}\)
a, \(\left(3x-1\right)\left(2x+7\right)-\left(x+1\right)\left(6x-5\right)=16\)
\(\Leftrightarrow6x^2+19x-7-\left(6x^2+x-5\right)=16\Leftrightarrow18x-2=16\Leftrightarrow x=1\)
b, \(x\left(x+1\right)\left(x+6\right)-x^3=5x\)
\(\Leftrightarrow\left(x^2+x\right)\left(x+6\right)-x^3=5x\Leftrightarrow x^3+7x^2+6x-x^3-5x=0\)
\(\Leftrightarrow7x^2+x=0\Leftrightarrow x=0;x=-\dfrac{1}{7}\)
c, \(\left(10x+9\right)x-\left(5x-1\right)\left(2x+3\right)=8\)
\(\Leftrightarrow10x^2+9x-\left(10x^2+13x-3\right)=8\Leftrightarrow-4x=5\Leftrightarrow x=-\dfrac{5}{4}\)
d, \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)=4\)
\(\Leftrightarrow21x-15x^2-35+25x-\left(10x-15x^2+4-6x\right)=4\)
\(\Leftrightarrow42x-43=0\Leftrightarrow x=\dfrac{43}{42}\)
e, \(\left(3x-5\right)\left(7-5x\right)+\left(5x+2\right)\left(3x-2\right)-2=0\)
\(\Leftrightarrow21x-15x^2-35+25x+\left(15x^2-10x+6x-4\right)-2=0\)
\(\Leftrightarrow30x-41=0\Leftrightarrow x=\dfrac{41}{30}\)
