4p(-7p+13)=6-(10p-4)

Solution for 4p(-7p+13)=6-(10p-4) equation:

Simplifying
4p(-7p + 13) = 6 + -1(10p + -4)

Reorder the terms:
4p(13 + -7p) = 6 + -1(10p + -4)
(13 * 4p + -7p * 4p) = 6 + -1(10p + -4)
(52p + -28p2) = 6 + -1(10p + -4)

Reorder the terms:
52p + -28p2 = 6 + -1(-4 + 10p)
52p + -28p2 = 6 + (-4 * -1 + 10p * -1)
52p + -28p2 = 6 + (4 + -10p)

Combine like terms: 6 + 4 = 10
52p + -28p2 = 10 + -10p

Solving
52p + -28p2 = 10 + -10p

Solving for variable 'p'.

Reorder the terms:
-10 + 52p + 10p + -28p2 = 10 + -10p + -10 + 10p

Combine like terms: 52p + 10p = 62p
-10 + 62p + -28p2 = 10 + -10p + -10 + 10p

Reorder the terms:
-10 + 62p + -28p2 = 10 + -10 + -10p + 10p

Combine like terms: 10 + -10 = 0
-10 + 62p + -28p2 = 0 + -10p + 10p
-10 + 62p + -28p2 = -10p + 10p

Combine like terms: -10p + 10p = 0
-10 + 62p + -28p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 31p + -14p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 31p + -14p2)' equal to zero and attempt to solve:

Simplifying
-5 + 31p + -14p2 = 0

Solving
-5 + 31p + -14p2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
0.3571428571 + -2.214285714p + p2 = 0

Move the constant term to the right:

Add '-0.3571428571' to each side of the equation.
0.3571428571 + -2.214285714p + -0.3571428571 + p2 = 0 + -0.3571428571

Reorder the terms:
0.3571428571 + -0.3571428571 + -2.214285714p + p2 = 0 + -0.3571428571

Combine like terms: 0.3571428571 + -0.3571428571 = 0.0000000000
0.0000000000 + -2.214285714p + p2 = 0 + -0.3571428571
-2.214285714p + p2 = 0 + -0.3571428571

Combine like terms: 0 + -0.3571428571 = -0.3571428571
-2.214285714p + p2 = -0.3571428571

The p term is -2.214285714p.  Take half its coefficient (-1.107142857).
Square it (1.225765306) and add it to both sides.

Add '1.225765306' to each side of the equation.
-2.214285714p + 1.225765306 + p2 = -0.3571428571 + 1.225765306

Reorder the terms:
1.225765306 + -2.214285714p + p2 = -0.3571428571 + 1.225765306

Combine like terms: -0.3571428571 + 1.225765306 = 0.8686224489
1.225765306 + -2.214285714p + p2 = 0.8686224489

Factor a perfect square on the left side:
(p + -1.107142857)(p + -1.107142857) = 0.8686224489

Calculate the square root of the right side: 0.931999168

Break this problem into two subproblems by setting 
(p + -1.107142857) equal to 0.931999168 and -0.931999168.

Subproblem 1
p + -1.107142857 = 0.931999168

Simplifying
p + -1.107142857 = 0.931999168

Reorder the terms:
-1.107142857 + p = 0.931999168

Solving
-1.107142857 + p = 0.931999168

Solving for variable 'p'.

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

Add '1.107142857' to each side of the equation.
-1.107142857 + 1.107142857 + p = 0.931999168 + 1.107142857

Combine like terms: -1.107142857 + 1.107142857 = 0.000000000
0.000000000 + p = 0.931999168 + 1.107142857
p = 0.931999168 + 1.107142857

Combine like terms: 0.931999168 + 1.107142857 = 2.039142025
p = 2.039142025

Simplifying
p = 2.039142025

Subproblem 2
p + -1.107142857 = -0.931999168

Simplifying
p + -1.107142857 = -0.931999168

Reorder the terms:
-1.107142857 + p = -0.931999168

Solving
-1.107142857 + p = -0.931999168

Solving for variable 'p'.

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

Add '1.107142857' to each side of the equation.
-1.107142857 + 1.107142857 + p = -0.931999168 + 1.107142857

Combine like terms: -1.107142857 + 1.107142857 = 0.000000000
0.000000000 + p = -0.931999168 + 1.107142857
p = -0.931999168 + 1.107142857

Combine like terms: -0.931999168 + 1.107142857 = 0.175143689
p = 0.175143689

Simplifying
p = 0.175143689

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.039142025, 0.175143689}
Solution
p = {2.039142025, 0.175143689}