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$x^4-7x^2+6=0\\ x^2=t\\ t^2-7t+6=0\\ D=49-24=25; \sqrt{D}=5\\ t_{1/2}= \frac{7\pm5}{2}\\ t_1=1\\ t_2=6\\\\ x^2=1\\ x_1=-1\\ x_2=1\\\\ x^2=6\\ x_3=- \sqrt{6} \\ x_3= \sqrt{6}\\\\\\ x^4+10x^2-11=0\\ x^2=t\\ t^2+10t-11=0\\ D=100+44=144; \sqrt{D} =12\\ t_{1/2}= \frac{-10\pm12}{2}\\ t_1=-11\\ t_2=1\\\\ x^2=1\\ x_1=-1\\ x_2=1\\\\ x^2=-11\\ x=\varnothing$

$\frac{5+2x}{4x-3} = \frac{3x+3}{7-x} \\\\ (5+2x)(7-x)=(3x+3)(4x-3)\\ -2x^2+9x+35=12x^2+3x-9\\ 14x^2-6x-44=0\ \ |:2\\ 7x^2-3x-22=0\\ D=9+616=625; \sqrt{D} =25\\ x_{1/2}= \frac{3\pm25}{14}\\ x_1=2\\ x_2=- \frac{11}{7}$

$(x^2-3x)^2-14(x^2-3x)+40=0\\ x^4-6x^3+9x^2-14x^2+42x+40=0\\ x^4-6x^3-5x^2+42x+40=0\\ (x^3-7x^2+2x+40)(x+1)=0\\ (x^2-9x+20)(x+1)(x+2)=0\\\\ x^2-9x+20=0\\ D=81-80=1; \sqrt{D} =1\\ x_{1/2}= \frac{9\pm1}{2}\\\\ x_1=4;x_2=5\\\\ x+1=0\\ x_3=-1\\\\ x+2=0\\ x_4=-2$

$x_6-9x^3+8=0\\ x^3=t\\ t^2-9t+8=0\\ D=81-32=49; \sqrt{D}=7\\ t_{1/2}= \frac{9\pm7}{2} \\ t_1=1\\ t_2=8\\\\ x^3=1\\ x_1=1\\\\ x^3=8\\ x^3=2^3\\ x_2=2$

$x(x-1)(x-2)=(x+1)(x+2)(x+3)\\ x(x^2-3x+2)=(x^2+3x+2)(x+3)\\ x^3-3x^2+2x=x^3+6x^2+11x+6\\ 6x^2+3x^2+11x-2x+6=0\\ 9x^2+9x+6=0\ \ |:3\\ 3x^2+3x+2=0\\ D=9-24=-15; \sqrt{D}\ \textless \ 0\\ x=\varnothing$
Нет действительных решений