First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#(3.5 xx x) - (3.5 xx 5.6) + 0.03x = 4.2x - 25.5#

#3.5x - 19.6 + 0.03x = 4.2x - 25.5#

Next, we can group and combine like terms on the left side of the equation:

#3.5x + 0.03x - 19.6 = 4.2x - 25.5#

#(3.5 + 0.03)x - 19.6 = 4.2x - 25.5#

#3.53x - 19.6 = 4.2x - 25.5#

Then, subtract #color(red)(3.53x)# and add #color(blue)(25.5)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#3.53x - 19.6 - color(red)(3.53x) + color(blue)(25.5) = 4.2x - 25.5 - color(red)(3.53x) + color(blue)(25.5)#

#3.53x - color(red)(3.53x) - 19.6 + color(blue)(25.5) = 4.2x - color(red)(3.53x) - 25.5 + color(blue)(25.5)#

#0 + 5.9 = (4.2 - color(red)(3.53))x - 0#

#5.9 = 0.67x#

Now, divide each side of the equation by #color(red)(0.67)# to solve for #x# while keeping the equation balanced:

#5.9/color(red)(0.67) = (0.67x)/color(red)(0.67)#

#8.806 = (color(red)(cancel(color(black)(0.67)))x)/cancel(color(red)(0.67))#

#8.806 = x#

#x = 8.806# rounded to the nearest thousandth.