How do you solve #10b^2 = 27b - 18# by factoring?

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Answer 1 · 2015-08-21T07:03:36

The solutions are:
#color(blue)(b=6/5#

# color(blue)(b=3/2#

#10b^2-27b+18=0#

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

In this technique we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 10*18 = 180#
and
#N_1 +N_2 = b =-27#

After trying out a few numbers we get #N_1 = -12# and #N_2 =-15#

#(-12)*(-15) = 180#, and #(-12)+(-15)= -27#

#10b^2-27b+18=10b^2-15b-12b+18#

#10b^2-15b-12b+18=0#

#5b(2b-3) -6(2b-3)=0#

#(5b-6)(2b-3)=0# is the factorised form of the expression.

Now we equate the factors to zero.

#5b-6=0, color(blue)(b=6/5#

#2b-3=0, color(blue)(b=3/2#