(7p-25)(p+7)+(p-6)(p+6)=

Solution for (7p-25)(p+7)+(p-6)(p+6)= equation:

Simplifying
(7p + -25)(p + 7) + (p + -6)(p + 6) = 0

Reorder the terms:
(-25 + 7p)(p + 7) + (p + -6)(p + 6) = 0

Reorder the terms:
(-25 + 7p)(7 + p) + (p + -6)(p + 6) = 0

Multiply (-25 + 7p) * (7 + p)
(-25(7 + p) + 7p * (7 + p)) + (p + -6)(p + 6) = 0
((7 * -25 + p * -25) + 7p * (7 + p)) + (p + -6)(p + 6) = 0
((-175 + -25p) + 7p * (7 + p)) + (p + -6)(p + 6) = 0
(-175 + -25p + (7 * 7p + p * 7p)) + (p + -6)(p + 6) = 0
(-175 + -25p + (49p + 7p2)) + (p + -6)(p + 6) = 0

Combine like terms: -25p + 49p = 24p
(-175 + 24p + 7p2) + (p + -6)(p + 6) = 0

Reorder the terms:
-175 + 24p + 7p2 + (-6 + p)(p + 6) = 0

Reorder the terms:
-175 + 24p + 7p2 + (-6 + p)(6 + p) = 0

Multiply (-6 + p) * (6 + p)
-175 + 24p + 7p2 + (-6(6 + p) + p(6 + p)) = 0
-175 + 24p + 7p2 + ((6 * -6 + p * -6) + p(6 + p)) = 0
-175 + 24p + 7p2 + ((-36 + -6p) + p(6 + p)) = 0
-175 + 24p + 7p2 + (-36 + -6p + (6 * p + p * p)) = 0
-175 + 24p + 7p2 + (-36 + -6p + (6p + p2)) = 0

Combine like terms: -6p + 6p = 0
-175 + 24p + 7p2 + (-36 + 0 + p2) = 0
-175 + 24p + 7p2 + (-36 + p2) = 0

Reorder the terms:
-175 + -36 + 24p + 7p2 + p2 = 0

Combine like terms: -175 + -36 = -211
-211 + 24p + 7p2 + p2 = 0

Combine like terms: 7p2 + p2 = 8p2
-211 + 24p + 8p2 = 0

Solving
-211 + 24p + 8p2 = 0

Solving for variable 'p'.

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

Divide each side by '8'.
-26.375 + 3p + p2 = 0

Move the constant term to the right:

Add '26.375' to each side of the equation.
-26.375 + 3p + 26.375 + p2 = 0 + 26.375

Reorder the terms:
-26.375 + 26.375 + 3p + p2 = 0 + 26.375

Combine like terms: -26.375 + 26.375 = 0.000
0.000 + 3p + p2 = 0 + 26.375
3p + p2 = 0 + 26.375

Combine like terms: 0 + 26.375 = 26.375
3p + p2 = 26.375

The p term is 3p.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3p + 2.25 + p2 = 26.375 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 26.375 + 2.25

Combine like terms: 26.375 + 2.25 = 28.625
2.25 + 3p + p2 = 28.625

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 28.625

Calculate the square root of the right side: 5.35023364

Break this problem into two subproblems by setting 
(p + 1.5) equal to 5.35023364 and -5.35023364.

Subproblem 1
p + 1.5 = 5.35023364

Simplifying
p + 1.5 = 5.35023364

Reorder the terms:
1.5 + p = 5.35023364

Solving
1.5 + p = 5.35023364

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = 5.35023364 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = 5.35023364 + -1.5
p = 5.35023364 + -1.5

Combine like terms: 5.35023364 + -1.5 = 3.85023364
p = 3.85023364

Simplifying
p = 3.85023364

Subproblem 2
p + 1.5 = -5.35023364

Simplifying
p + 1.5 = -5.35023364

Reorder the terms:
1.5 + p = -5.35023364

Solving
1.5 + p = -5.35023364

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = -5.35023364 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = -5.35023364 + -1.5
p = -5.35023364 + -1.5

Combine like terms: -5.35023364 + -1.5 = -6.85023364
p = -6.85023364

Simplifying
p = -6.85023364

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.85023364, -6.85023364}