Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. Use $e=2.71828182845905$.
\[
e^{3 x+14}=146^{4 x+11}
\]

Step 1 ：Take the natural logarithm (ln) of both sides of the equation to get rid of the exponential: \(\ln(e^{3x+14}) = \ln(146^{4x+11})\)

Step 2 ：Use the property of logarithms that allows us to bring down exponents: \((3x+14)\ln(e) = (4x+11)\ln(146)\)

Step 3 ：Simplify the equation since the natural logarithm of e is 1: \(3x+14 = (4x+11)\ln(146)\)

Step 4 ：Isolate the terms with x on one side of the equation: \(3x - (4x\ln(146)) = 11\ln(146) - 14\)

Step 5 ：Factor out x: \(x(3 - 4\ln(146)) = 11\ln(146) - 14\)

Step 6 ：Solve for x by dividing both sides by (3 - 4ln(146)): \(x = \frac{11\ln(146) - 14}{3 - 4\ln(146)}\)

Step 7 ：Substitute the given value for e into the natural logarithm and perform the calculation to find the decimal approximation: \(x \approx \frac{11\ln(146) - 14}{3 - 4\ln(146)} \approx -0.97\)

Step 8 ：The solution to the equation is \(\boxed{x = -0.97}\) (rounded to two decimal places)