The equation to be solved for p is : (4p-1)^2 = -5(4p-1)-6

(4p-1)^2 = -5(4p-1)-6

expand the left hand side using (a + b)^2 = a^2 + 2ab + b^2 and open the brackets on the right and multiply.

=> 16p^2 + 1 - 8p = -20p + 5 - 6

=> 16p^2 + 12p + 2 = 0

=> 8p^2 + 6p + 1 = 0

=> 8p^2 + 4p + 2p + 1 = 0

=> 4p(2p + 1) + 1(2p + 1) = 0

=> (4p + 1)(2p + 1) = 0

4p + 1 = 0

=> p = -1/4

2p + 1 = 0

=> p = -1/2

**The solution to the equation is p = -1/4 and p = -1/2**

(4p-1)^2 = -5(4p-1) -6

First we will open the brackets.

==> 16p^2 - 8p + 1 = -20p + 5 - 6

Now we will combine like terms.

==> 16p^2 +12p +2 = 0

Now we will divide by 2.

==> 8p + 6p + 1 = 0

Now we will find the roots using the quadratic formula.

==> p1 = (-6 + sqrt( 36-32) / 16 = ( -6 + 2)/16 = -4/16 = -1/4

==> p2 = (-6-2)/16) = -8/16 = -1/2

Then we have two values for P.

**==> p= { -1/2, -1/4)**