Number of Solutions of Absolute Equation

$x = 0$ is a solution. For $x \ne 0$, divide by $x^2$: $\frac{|x|(6x^2+1)}{x^2} = 5 \implies \frac{6x^2+1}{|x|} = 5$. Let $t = |x| > 0$. $\frac{6t^2 + 1}{t} = 5 \implies 6t^2 - 5t + 1 = 0 \implies (2t - 1)(3t - 1) = 0$. $t = 1/2$ or $t = 1/3$. Since $t = |x|$, $x = \pm 1/2$ and $x = \pm 1/3$. Total solutions $= 1 + 2 + 2 = 5$.