How do you solve #15a^2 - 3a = 3 - 7a# by factoring?

1 Answer
Aug 21, 2015

Answer:

The solutions are

#color(blue)(a=1/3#

# color(blue)(a=-3/5#

Explanation:

#15a^2−3a=3−7a#

#15a^2−3a+7a-3=0#

#15a^2+4a-3=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 = 15*-3 = -45#
AND
#N_1 +N_2 = b = 4#

After trying out a few numbers we get #N_1 = 9# and #N_2 =-5#
#9*-5 = -45#, and #9+(-5)= 4#

#15a^2+4a-3=15a^2+9a-5a-3#

#15a^2+9a-5a-3=0#

#3a(5a+3) -1(5a+3)=0#
#(3a-1)(5a+3) =0# is the factorised form of the equation.

Now we equate factors to zero.
#3a-1 = 0, color(blue)(a=1/3#

#5a+3 = 0, color(blue)(a=-3/5#