How do you evaluate #(3x - 2) \cdot ( 5x + 3) = - x ^ { 2} +4x^2#?

1 Answer
Jim G.
Jun 23, 2018

#x=-2/3" or "x=3/4#

Explanation:

#"expand the factors on the left side of the equation"#

#15x^2-x-6=3x^2#

#"subtract "3x^2" from both sides"#

#12x^2-x-6=0larrcolor(blue)"in standard form"#

#"factor the quadratic using the a-c method"#

#"the factors of the product "12xx-6=-72#

#"which sum to "-1" are "+8" and "-9#

#"split the middle term using these factors"#

#12x^2+8x-9x-6=0larrcolor(blue)"factor by grouping"#

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

#"take out the "color(blue)"common factor "(3x+2)#

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

#"equate each factor to zero and solve for "x#

#3x+2=0rArrx=-2/3#

#4x-3=0rArrx=3/4#

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