2x²+5|x|=0

To solve the equation \(2x^2 + 5|x| = 0\), we need to consider the absolute value. The expression \(5|x|\) is non-negative because absolute values are always non-negative, and \(2x^2\) is also non-negative since it is a square term multiplied by a positive constant.

Thus, the left-hand side of the equation \(2x^2 + 5|x|\) can only equal zero if both terms are individually zero. Therefore, we set each term to zero:

1. First term: \[ 2x^2 = 0 \implies x^2 = 0 \implies x = 0 \]

2. Second term: \[ 5|x| = 0 \implies |x| = 0 \implies x = 0 \]

Both conditions lead to the same solution:

\[ x = 0 \]

Thus, the only solution to the equation \(2x^2 + 5|x| = 0\) is

\[ \boxed{0}. \]