How do you factor #4x^2+7x=2#?

1 Answer
May 23, 2018

Answer:

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

Explanation:

We can subtract #2# from both sides of this equation to set it equal to zero. We get

#4x^2+7x-2=0#

Now, we can factor by grouping. Here, we will split up the #b# term into two separate terms so we can factor more easily. We can rewrite this business as

#color(blue)(4x^2+8x)color(red)(-x-2)=0#

Notice, I rewrote #7x# as being equal to #8x-x#, so I didn't change the value of the expression.

We can factor out a #4x# out of the blue terms, and a #-1# out of the red terms. We get

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

Both terms have an #(x+2)# in common, so we can factor that out to get

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

as our complete, factored answer.

Hope this helps!