-14p(5-3p)=2(p-5)-4

Solution for -14p(5-3p)=2(p-5)-4 equation:

Simplifying
-14p(5 + -3p) = 2(p + -5) + -4
(5 * -14p + -3p * -14p) = 2(p + -5) + -4
(-70p + 42p2) = 2(p + -5) + -4

Reorder the terms:
-70p + 42p2 = 2(-5 + p) + -4
-70p + 42p2 = (-5 * 2 + p * 2) + -4
-70p + 42p2 = (-10 + 2p) + -4

Reorder the terms:
-70p + 42p2 = -10 + -4 + 2p

Combine like terms: -10 + -4 = -14
-70p + 42p2 = -14 + 2p

Solving
-70p + 42p2 = -14 + 2p

Solving for variable 'p'.

Reorder the terms:
14 + -70p + -2p + 42p2 = -14 + 2p + 14 + -2p

Combine like terms: -70p + -2p = -72p
14 + -72p + 42p2 = -14 + 2p + 14 + -2p

Reorder the terms:
14 + -72p + 42p2 = -14 + 14 + 2p + -2p

Combine like terms: -14 + 14 = 0
14 + -72p + 42p2 = 0 + 2p + -2p
14 + -72p + 42p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
14 + -72p + 42p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -36p + 21p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -36p + 21p2)' equal to zero and attempt to solve:

Simplifying
7 + -36p + 21p2 = 0

Solving
7 + -36p + 21p2 = 0

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

Divide each side by '21'.
0.3333333333 + -1.714285714p + p2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.714285714p + -0.3333333333 + p2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.714285714p + p2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.714285714p + p2 = 0 + -0.3333333333
-1.714285714p + p2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.714285714p + p2 = -0.3333333333

The p term is -1.714285714p.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714p + 0.7346938773 + p2 = -0.3333333333 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714p + p2 = -0.3333333333 + 0.7346938773

Combine like terms: -0.3333333333 + 0.7346938773 = 0.401360544
0.7346938773 + -1.714285714p + p2 = 0.401360544

Factor a perfect square on the left side:
(p + -0.857142857)(p + -0.857142857) = 0.401360544

Calculate the square root of the right side: 0.633530223

Break this problem into two subproblems by setting 
(p + -0.857142857) equal to 0.633530223 and -0.633530223.

Subproblem 1
p + -0.857142857 = 0.633530223

Simplifying
p + -0.857142857 = 0.633530223

Reorder the terms:
-0.857142857 + p = 0.633530223

Solving
-0.857142857 + p = 0.633530223

Solving for variable 'p'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + p = 0.633530223 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + p = 0.633530223 + 0.857142857
p = 0.633530223 + 0.857142857

Combine like terms: 0.633530223 + 0.857142857 = 1.49067308
p = 1.49067308

Simplifying
p = 1.49067308

Subproblem 2
p + -0.857142857 = -0.633530223

Simplifying
p + -0.857142857 = -0.633530223

Reorder the terms:
-0.857142857 + p = -0.633530223

Solving
-0.857142857 + p = -0.633530223

Solving for variable 'p'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + p = -0.633530223 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + p = -0.633530223 + 0.857142857
p = -0.633530223 + 0.857142857

Combine like terms: -0.633530223 + 0.857142857 = 0.223612634
p = 0.223612634

Simplifying
p = 0.223612634

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.49067308, 0.223612634}
Solution
p = {1.49067308, 0.223612634}