How do you solve #6x^2 + 5x - 4 = 0# by factoring?

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Answer 1 · 2015-08-17T06:35:15

The solutions are
# color(blue)(x=-4/3#

#color(blue)(x=1/2#

#6x^2+5x−4=0 #

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 6*-4 = -24#
and
#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 8# and #N_2 =-3#
#8*-3 = -24#, and #8+(-3)= 5#

#6x^2+5x−4=6x^2-3x+8x−4#

#=3x(2x-1) +4(2x-1)=0#

#=(3x+4)(2x-1) =0#

Now we equate the factors to zero.
#=3x+4 =0, color(blue)(x=-4/3#

#=2x-1 =0, color(blue)(x=1/2#