\(x^4=x\)
\(\Rightarrow x=1\)
\(\left(2x+1\right)^3=125\)
\(\Rightarrow\left(2x+1\right)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow2x=5-1=4\)
\(\Rightarrow x=4:2=2\)
\(2^{3x}+4=132\)
\(\Rightarrow2^{3x}=132-4=128\)
\(\Rightarrow2^{3x}=2^7\)
\(\Rightarrow3x=7\)
\(\Rightarrow x=7:3=\frac{7}{3}\)