Algebraically solve the equation, $\left(4^{5 x+3}\right)^{2}=4$, for $x$. All answers should be exact. If there is more than one solution, separate them by commas. If there is no solution, type DNE. \[ x= \] Submit Answer MY NOTES

Step 1 ：\(\left(4^{5x+3}\right)^{2}=4^{2(5x+3)}=4^{10x+6}\)

Step 2 ：\(4=2^2\), so we can rewrite the equation as \((2^2)^{10x+6}=2^2\)

Step 3 ：This simplifies to \(2^{20x+12}=2^2\)

Step 4 ：Since the bases are equal, the exponents must also be equal. Therefore, we can set up the equation \(20x+12=2\)

Step 5 ：Solving for \(x\) gives \(20x=2-12\)

Step 6 ：\(20x=-10\)

Step 7 ：\(x=-10/20\)

Step 8 ：\(\boxed{x=-0.5}\)