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x*3^(x-1)+3*3^sqr(3-x)=3^x+x*3^sqr(3-x) equation

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Numerical solution:

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The solution

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              /       2\           /       2\
   x - 1      \(3 - x) /    x      \(3 - x) /
x*3      + 3*3           = 3  + x*3          
$$3 \cdot 3^{\left(3 - x\right)^{2}} + 3^{x - 1} x = 3^{x} + 3^{\left(3 - x\right)^{2}} x$$
The graph
Sum and product of roots [src]
sum
2 + 3 + 5
$$\left(2 + 3\right) + 5$$
=
10
$$10$$
product
2*3*5
$$5 \cdot 2 \cdot 3$$
=
30
$$30$$
30
Rapid solution [src]
x1 = 2
$$x_{1} = 2$$
x2 = 3
$$x_{2} = 3$$
x3 = 5
$$x_{3} = 5$$
x3 = 5
Numerical answer [src]
x1 = 5.0
x2 = 3.0
x3 = 2.0
x3 = 2.0