How do you solve #u(u - 5) + 8u = u(u + 2) - 4 #?

1 Answer
May 27, 2017

Answer:

See a solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(u)(u - 5) + 8u = color(blue)(u)(u + 2) - 4#

#(color(red)(u) xx u) - (color(red)(u) xx 5) + 8u = (color(blue)(u) xx u) + (color(blue)(u) xx 2) - 4#

#u^2 - 5u + 8u = u^2 + 2u - 4#

#u^2 + (-5 + 8)u = u^2 + 2u - 4#

#u^2 + 3u = u^2 + 2u - 4#

Next, subtract #color(red)(u^2)# from each side of the equation to eliminate this term while keeping the equation balanced:

#-color(red)(u^2) + u^2 + 3u = -color(red)(u^2) + u^2 + 2u - 4#

#0 + 3u = 0 + 2u - 4#

#3u = 2u - 4#

Now, subtract #color(red)(2u)# from each side of the equation to solve for #u# while keeping the equation balanced:

#-color(red)(2u) + 3u = -color(red)(2u) + 2u - 4#

#(-color(red)(2) + 3)u = 0 - 4#

#1u = -4#

#u = -4#