How do you solve #4x^2+6x=0# by factoring?

2 Answers
MathFact-orials.blogspot.com
Jun 28, 2018

#x=0, -3/2#

Explanation:

Notice that we can factor out #2x# from both terms on the LH side:

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

#:. 2x=0, 2x+3=0#

For #2x=0=>color(blue)(bar(ul(abs(color(black)(x=0#

For #2x+3=0#

#2x=-3=>color(blue)(bar(ul(abs(color(black)(x=-3/2#

We can see these in the graph:

graph{4x^2+6x}

Meave60
Jun 28, 2018

#x=0#, #-3/2#

Explanation:

Solve:

#4x^2+6x=0#

The greatest common factor of #4# and #6# is #2#. The greatest common factor of #x^2# and #x# is #x#. The greatest common factor is #2x#. Factor out #2x#.

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

#2x=0#

#x=0/2#

#x=0#

#2x+3=0#

#2x=-3#

#x=-3/2#

Solutions for #x#.

#x=0#, #-3/2#

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