Question

6⁴:6²+6x(66-x:6)=6³
???​

Answer 1

$6 {}^{4} : 6 {}^{2} + 6x(6 - x : 6) = 6 {}^{3} \\ 6 {}^{2} + 36x - x {}^{2} = 6 {}^{3} \\ 36x - x {}^{2} = 216 - 36 \\ 36x - x {}^{2} = 180 \\ - 180 + 36x - x {}^{2} = 0 \\ 180 - 36x + x {}^{2} = 0 \\ x {}^{2} - 36x + 180 = 0 \\ x {}^{2} - 6x - 30x + 180 = 0 \\ x(x - 6) - 30(x - 6) = 0 \\ (x - 30)(x - 6) = 0 \\ \\ \iff \: x - 30 = 0\implies \: \color{pink}x _{1} = 30 \\ \iff \: x - 6 = 0\implies \: \color{pink}x_{2} = 6$