-3(2p+1)4(2p-3)=2p-15

Solution for -3(2p+1)4(2p-3)=2p-15 equation:

Simplifying
-3(2p + 1) * 4(2p + -3) = 2p + -15

Reorder the terms:
-3(1 + 2p) * 4(2p + -3) = 2p + -15

Reorder the terms:
-3(1 + 2p) * 4(-3 + 2p) = 2p + -15

Reorder the terms for easier multiplication:
-3 * 4(1 + 2p)(-3 + 2p) = 2p + -15

Multiply -3 * 4
-12(1 + 2p)(-3 + 2p) = 2p + -15

Multiply (1 + 2p) * (-3 + 2p)
-12(1(-3 + 2p) + 2p * (-3 + 2p)) = 2p + -15
-12((-3 * 1 + 2p * 1) + 2p * (-3 + 2p)) = 2p + -15
-12((-3 + 2p) + 2p * (-3 + 2p)) = 2p + -15
-12(-3 + 2p + (-3 * 2p + 2p * 2p)) = 2p + -15
-12(-3 + 2p + (-6p + 4p2)) = 2p + -15

Combine like terms: 2p + -6p = -4p
-12(-3 + -4p + 4p2) = 2p + -15
(-3 * -12 + -4p * -12 + 4p2 * -12) = 2p + -15
(36 + 48p + -48p2) = 2p + -15

Reorder the terms:
36 + 48p + -48p2 = -15 + 2p

Solving
36 + 48p + -48p2 = -15 + 2p

Solving for variable 'p'.

Reorder the terms:
36 + 15 + 48p + -2p + -48p2 = -15 + 2p + 15 + -2p

Combine like terms: 36 + 15 = 51
51 + 48p + -2p + -48p2 = -15 + 2p + 15 + -2p

Combine like terms: 48p + -2p = 46p
51 + 46p + -48p2 = -15 + 2p + 15 + -2p

Reorder the terms:
51 + 46p + -48p2 = -15 + 15 + 2p + -2p

Combine like terms: -15 + 15 = 0
51 + 46p + -48p2 = 0 + 2p + -2p
51 + 46p + -48p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
51 + 46p + -48p2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-1.0625 + -0.9583333333p + p2 = 0

Move the constant term to the right:

Add '1.0625' to each side of the equation.
-1.0625 + -0.9583333333p + 1.0625 + p2 = 0 + 1.0625

Reorder the terms:
-1.0625 + 1.0625 + -0.9583333333p + p2 = 0 + 1.0625

Combine like terms: -1.0625 + 1.0625 = 0.0000
0.0000 + -0.9583333333p + p2 = 0 + 1.0625
-0.9583333333p + p2 = 0 + 1.0625

Combine like terms: 0 + 1.0625 = 1.0625
-0.9583333333p + p2 = 1.0625

The p term is -0.9583333333p.  Take half its coefficient (-0.4791666667).
Square it (0.2296006945) and add it to both sides.

Add '0.2296006945' to each side of the equation.
-0.9583333333p + 0.2296006945 + p2 = 1.0625 + 0.2296006945

Reorder the terms:
0.2296006945 + -0.9583333333p + p2 = 1.0625 + 0.2296006945

Combine like terms: 1.0625 + 0.2296006945 = 1.2921006945
0.2296006945 + -0.9583333333p + p2 = 1.2921006945

Factor a perfect square on the left side:
(p + -0.4791666667)(p + -0.4791666667) = 1.2921006945

Calculate the square root of the right side: 1.136706072

Break this problem into two subproblems by setting 
(p + -0.4791666667) equal to 1.136706072 and -1.136706072.

Subproblem 1
p + -0.4791666667 = 1.136706072

Simplifying
p + -0.4791666667 = 1.136706072

Reorder the terms:
-0.4791666667 + p = 1.136706072

Solving
-0.4791666667 + p = 1.136706072

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.4791666667' to each side of the equation.
-0.4791666667 + 0.4791666667 + p = 1.136706072 + 0.4791666667

Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000
0.0000000000 + p = 1.136706072 + 0.4791666667
p = 1.136706072 + 0.4791666667

Combine like terms: 1.136706072 + 0.4791666667 = 1.6158727387
p = 1.6158727387

Simplifying
p = 1.6158727387

Subproblem 2
p + -0.4791666667 = -1.136706072

Simplifying
p + -0.4791666667 = -1.136706072

Reorder the terms:
-0.4791666667 + p = -1.136706072

Solving
-0.4791666667 + p = -1.136706072

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.4791666667' to each side of the equation.
-0.4791666667 + 0.4791666667 + p = -1.136706072 + 0.4791666667

Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000
0.0000000000 + p = -1.136706072 + 0.4791666667
p = -1.136706072 + 0.4791666667

Combine like terms: -1.136706072 + 0.4791666667 = -0.6575394053
p = -0.6575394053

Simplifying
p = -0.6575394053

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.6158727387, -0.6575394053}