How do you solve #3(4 - x)(2x + 1) = 0#?

1 Answer
May 15, 2017

Answer:

See a solution process below:

Explanation:

First, divide each side of the equation by #color(red)(3)# to eliminate the constant while keeping the equation balanced"

#(3(4 - x)(2x + 1))/color(red)(3) = 0/color(red)(3)#

#(color(red)(cancel(color(black)(3)))(4 - x)(2x + 1))/cancel(color(red)(3)) = 0#

#(4 - x)(2x + 1) = 0#

Solve each term on the left side of the equation for #0#:

Solution 1)

#4 - x = 0#

#-color(red)(4) + 4 - x = -color(red)(4) + 0#

#0 - x = -4#

#-x = -4#

#color(red)(-1) xx -x = color(red)(-1) xx -4#

#x = 4#

Solution 2)

#2x + 1 = 0#

#2x + 1 - color(red)(1) = 0 - color(red)(1)#

#2x + 0 = -1#

#2x = -1#

#(2x)/color(red)(2) = -1/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -1/2#

#x = -1/2#

The solutions are: #x = 4# and #x = -1/2#