How do you factor completely #3x^2+4x-4+=0#?

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Answer 1 · 2018-06-30T22:38:47

#x=-2# and #x=2/3#

We can use factoring by grouping. Here I will rewrite the #b# term as the sum of two terms so we can factor.

Our quadratic can be alternatively written as

#color(turquoise)(3x^2-2x)+color(orange)(6x-4)=0#

We can factor an #x# out of the light blue term, and a #2# out of the orange term. This gives us

#color(turquoise)(x(3x-2))+color(orange)(2(3x-2))=0#

We can factor out a #3x-2# to get

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

Setting both factors equal to zero, we get

#x=-2# and #x=2/3#

Hope this helps!