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

Question

20040 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-16T15:49:00

#x=1/2" or "x=-3#

For this equation to become the value of zero it means that either the left bracket is zero or the right bracket is zero.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider #color(blue)((2x-1)=0)#

#color(magenta)("Detailed calculation to show how it works")#

Add #color(red)( 1)# to both sides

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

#" "color(blue)(2x+0=1)#

Divide both sides by #color(red)(2)#

#" "color(blue)(2/(color(red)(2))xx x=1/(color(red)(2))#

But #2/2 = 1# giving

#x=1/2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider #color(blue)((x+3)=0)#

#color(magenta)("Calculation skipping steps")#

#x=-3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer 2 · 2016-03-16T15:53:32

#x# can equal #-1/2# or #-3#

#(2x-1)(x+3)=0#

To solve for the value of #x# simply take each of the binomial factors and set them equal to zero.

#2x+1 = 0#
#2xcancel(+1)cancel-1 = 0-1#
#(cancel2x)/cancel2 =-1/2#
#x=-1/2#

#x+3 = 0#
#xcancel(+3)cancel-3 = 0-3#
#x=-3#

#x# can equal #-1/2# or #-3#