2p(p-1)-(3p+5)(-7p-4)=

Solution for 2p(p-1)-(3p+5)(-7p-4)= equation:

Simplifying
2p(p + -1) + -1(3p + 5)(-7p + -4) = 0

Reorder the terms:
2p(-1 + p) + -1(3p + 5)(-7p + -4) = 0
(-1 * 2p + p * 2p) + -1(3p + 5)(-7p + -4) = 0
(-2p + 2p2) + -1(3p + 5)(-7p + -4) = 0

Reorder the terms:
-2p + 2p2 + -1(5 + 3p)(-7p + -4) = 0

Reorder the terms:
-2p + 2p2 + -1(5 + 3p)(-4 + -7p) = 0

Multiply (5 + 3p) * (-4 + -7p)
-2p + 2p2 + -1(5(-4 + -7p) + 3p * (-4 + -7p)) = 0
-2p + 2p2 + -1((-4 * 5 + -7p * 5) + 3p * (-4 + -7p)) = 0
-2p + 2p2 + -1((-20 + -35p) + 3p * (-4 + -7p)) = 0
-2p + 2p2 + -1(-20 + -35p + (-4 * 3p + -7p * 3p)) = 0
-2p + 2p2 + -1(-20 + -35p + (-12p + -21p2)) = 0

Combine like terms: -35p + -12p = -47p
-2p + 2p2 + -1(-20 + -47p + -21p2) = 0
-2p + 2p2 + (-20 * -1 + -47p * -1 + -21p2 * -1) = 0
-2p + 2p2 + (20 + 47p + 21p2) = 0

Reorder the terms:
20 + -2p + 47p + 2p2 + 21p2 = 0

Combine like terms: -2p + 47p = 45p
20 + 45p + 2p2 + 21p2 = 0

Combine like terms: 2p2 + 21p2 = 23p2
20 + 45p + 23p2 = 0

Solving
20 + 45p + 23p2 = 0

Solving for variable 'p'.

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

Divide each side by '23'.
0.8695652174 + 1.956521739p + p2 = 0

Move the constant term to the right:

Add '-0.8695652174' to each side of the equation.
0.8695652174 + 1.956521739p + -0.8695652174 + p2 = 0 + -0.8695652174

Reorder the terms:
0.8695652174 + -0.8695652174 + 1.956521739p + p2 = 0 + -0.8695652174

Combine like terms: 0.8695652174 + -0.8695652174 = 0.0000000000
0.0000000000 + 1.956521739p + p2 = 0 + -0.8695652174
1.956521739p + p2 = 0 + -0.8695652174

Combine like terms: 0 + -0.8695652174 = -0.8695652174
1.956521739p + p2 = -0.8695652174

The p term is 1.956521739p.  Take half its coefficient (0.9782608695).
Square it (0.9569943288) and add it to both sides.

Add '0.9569943288' to each side of the equation.
1.956521739p + 0.9569943288 + p2 = -0.8695652174 + 0.9569943288

Reorder the terms:
0.9569943288 + 1.956521739p + p2 = -0.8695652174 + 0.9569943288

Combine like terms: -0.8695652174 + 0.9569943288 = 0.0874291114
0.9569943288 + 1.956521739p + p2 = 0.0874291114

Factor a perfect square on the left side:
(p + 0.9782608695)(p + 0.9782608695) = 0.0874291114

Calculate the square root of the right side: 0.295684141

Break this problem into two subproblems by setting 
(p + 0.9782608695) equal to 0.295684141 and -0.295684141.

Subproblem 1
p + 0.9782608695 = 0.295684141

Simplifying
p + 0.9782608695 = 0.295684141

Reorder the terms:
0.9782608695 + p = 0.295684141

Solving
0.9782608695 + p = 0.295684141

Solving for variable 'p'.

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

Add '-0.9782608695' to each side of the equation.
0.9782608695 + -0.9782608695 + p = 0.295684141 + -0.9782608695

Combine like terms: 0.9782608695 + -0.9782608695 = 0.0000000000
0.0000000000 + p = 0.295684141 + -0.9782608695
p = 0.295684141 + -0.9782608695

Combine like terms: 0.295684141 + -0.9782608695 = -0.6825767285
p = -0.6825767285

Simplifying
p = -0.6825767285

Subproblem 2
p + 0.9782608695 = -0.295684141

Simplifying
p + 0.9782608695 = -0.295684141

Reorder the terms:
0.9782608695 + p = -0.295684141

Solving
0.9782608695 + p = -0.295684141

Solving for variable 'p'.

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

Add '-0.9782608695' to each side of the equation.
0.9782608695 + -0.9782608695 + p = -0.295684141 + -0.9782608695

Combine like terms: 0.9782608695 + -0.9782608695 = 0.0000000000
0.0000000000 + p = -0.295684141 + -0.9782608695
p = -0.295684141 + -0.9782608695

Combine like terms: -0.295684141 + -0.9782608695 = -1.2739450105
p = -1.2739450105

Simplifying
p = -1.2739450105

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.6825767285, -1.2739450105}