The equation to be solved is 5*6^x = 2*3^2x + 3*2^2x

5*6^x = 2*3^2x + 3*2^2x

=> 5 = 2*3^2x/6^x + 3*2^2x/6^x

=> 5 = 2*(3/2)^x + 3*(2/3)^x

let (3/2)^x = y

=> 5 = 2y + 3/y

=> 5y = 2y^2 + 3

=> 2y^2 - 5y + 3...

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The equation to be solved is 5*6^x = 2*3^2x + 3*2^2x

5*6^x = 2*3^2x + 3*2^2x

=> 5 = 2*3^2x/6^x + 3*2^2x/6^x

=> 5 = 2*(3/2)^x + 3*(2/3)^x

let (3/2)^x = y

=> 5 = 2y + 3/y

=> 5y = 2y^2 + 3

=> 2y^2 - 5y + 3 = 0

=> 2y^2 - 2y - 3y + 3 = 0

=> 2y(y - 1) - 3(y - 1) = 0

=> (2y - 3)(y - 1) = 0

y = 3/2 and y = 1

y = (3/2)^x

(3/2)^x = 3/2 for x = 1

(3/2)^x = 1 for x = 0

**The solution for the equation is x = 0 and x = 1**