By factoring out the x on the left side, we get:
x[1 - e^(5x + 2)] = 0.
So, by the zero-product property, either x = 0 or:
1 - e^(5x + 2) = 0 ==> e^(5x + 2) = 1 = e^0.
Comparing the exponents gives:
5x + 2 = 0 ==> x = -2/5.
Therefore, x = -2/5 and x = 0 are the required solutions.
I hope this helps!
x[1 - e^(5x + 2)] = 0.
So, by the zero-product property, either x = 0 or:
1 - e^(5x + 2) = 0 ==> e^(5x + 2) = 1 = e^0.
Comparing the exponents gives:
5x + 2 = 0 ==> x = -2/5.
Therefore, x = -2/5 and x = 0 are the required solutions.
I hope this helps!