x^2-4x+3=4x-13

x² - 4x + 3  =  4x - 13

Subtract  4x  from both sides:

x² - 8x + 3  =  -13

Add  13  to both sides:

x² - 8x + 16  =  0

Factor:

(x - 4)(x - 4)  =  0

So, either  x - 4  =  0  or  x - 4  =  0

--->               x  =  4    or     x  =  4

Obviously,  x  =  4.