7p(3p+4)=-2(2p+-1)+10

Solution for 7p(3p+4)=-2(2p+-1)+10 equation:

Simplifying
7p(3p + 4) = -2(2p + -1) + 10

Reorder the terms:
7p(4 + 3p) = -2(2p + -1) + 10
(4 * 7p + 3p * 7p) = -2(2p + -1) + 10
(28p + 21p2) = -2(2p + -1) + 10

Reorder the terms:
28p + 21p2 = -2(-1 + 2p) + 10
28p + 21p2 = (-1 * -2 + 2p * -2) + 10
28p + 21p2 = (2 + -4p) + 10

Reorder the terms:
28p + 21p2 = 2 + 10 + -4p

Combine like terms: 2 + 10 = 12
28p + 21p2 = 12 + -4p

Solving
28p + 21p2 = 12 + -4p

Solving for variable 'p'.

Reorder the terms:
-12 + 28p + 4p + 21p2 = 12 + -4p + -12 + 4p

Combine like terms: 28p + 4p = 32p
-12 + 32p + 21p2 = 12 + -4p + -12 + 4p

Reorder the terms:
-12 + 32p + 21p2 = 12 + -12 + -4p + 4p

Combine like terms: 12 + -12 = 0
-12 + 32p + 21p2 = 0 + -4p + 4p
-12 + 32p + 21p2 = -4p + 4p

Combine like terms: -4p + 4p = 0
-12 + 32p + 21p2 = 0

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

Divide each side by '21'.
-0.5714285714 + 1.523809524p + p2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 1.523809524p + 0.5714285714 + p2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 1.523809524p + p2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 1.523809524p + p2 = 0 + 0.5714285714
1.523809524p + p2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
1.523809524p + p2 = 0.5714285714

The p term is 1.523809524p.  Take half its coefficient (0.761904762).
Square it (0.5804988664) and add it to both sides.

Add '0.5804988664' to each side of the equation.
1.523809524p + 0.5804988664 + p2 = 0.5714285714 + 0.5804988664

Reorder the terms:
0.5804988664 + 1.523809524p + p2 = 0.5714285714 + 0.5804988664

Combine like terms: 0.5714285714 + 0.5804988664 = 1.1519274378
0.5804988664 + 1.523809524p + p2 = 1.1519274378

Factor a perfect square on the left side:
(p + 0.761904762)(p + 0.761904762) = 1.1519274378

Calculate the square root of the right side: 1.073278826

Break this problem into two subproblems by setting 
(p + 0.761904762) equal to 1.073278826 and -1.073278826.

Subproblem 1
p + 0.761904762 = 1.073278826

Simplifying
p + 0.761904762 = 1.073278826

Reorder the terms:
0.761904762 + p = 1.073278826

Solving
0.761904762 + p = 1.073278826

Solving for variable 'p'.

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

Add '-0.761904762' to each side of the equation.
0.761904762 + -0.761904762 + p = 1.073278826 + -0.761904762

Combine like terms: 0.761904762 + -0.761904762 = 0.000000000
0.000000000 + p = 1.073278826 + -0.761904762
p = 1.073278826 + -0.761904762

Combine like terms: 1.073278826 + -0.761904762 = 0.311374064
p = 0.311374064

Simplifying
p = 0.311374064

Subproblem 2
p + 0.761904762 = -1.073278826

Simplifying
p + 0.761904762 = -1.073278826

Reorder the terms:
0.761904762 + p = -1.073278826

Solving
0.761904762 + p = -1.073278826

Solving for variable 'p'.

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

Add '-0.761904762' to each side of the equation.
0.761904762 + -0.761904762 + p = -1.073278826 + -0.761904762

Combine like terms: 0.761904762 + -0.761904762 = 0.000000000
0.000000000 + p = -1.073278826 + -0.761904762
p = -1.073278826 + -0.761904762

Combine like terms: -1.073278826 + -0.761904762 = -1.835183588
p = -1.835183588

Simplifying
p = -1.835183588

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.311374064, -1.835183588}