How do you solve #5x^2 - 2x + 16 = 4x^2 + 6x#?

We have: #5 x^(2) - 2 x + 16 = 4 x^(2) + 6 x#

First, let's subtract #4 x^(2) + 6 x# from both sides of the equation:

#=> x^(2) - 8 x + 16 = 0#

Then, let's factorise the equation using the middle-term break:

#=> x^(2) - 4 x - 4 x + 16 = 0#

#=> x (x - 4) - 4 (x - 4) = 0#

#=> (x - 4) (x - 4) = 0#

#=> (x - 4)^(2) = 0#

#=> x - 4 = 0#

#=> x = 4#

Therefore, the solution to the equation is #x = 4#.