Find Exact Solutions of an Exponential Equation that is Quadratic in Form: 5^(2x)+125=30(5^x)

The exponential equation to be solved is: 5^(2x)+125=30(5^x). It is first shown that this equation is quadratic in form and it is solved by making the substitution u=5^x. This results in a quadratic equation in u that is solved by factoring. After the solutions are found for u, then u has to be replaced by 5^x. This gives two simple exponential equations that can be solved by making the bases the same.

Timestamps
0:00 Introduction
0:36 Show Equation is Quadratic in Form
1:32 Let u = 5^x and Solve for u
3:28 Solve for x