400=4p(18-(p-3))

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Solution for 400=4p(18-(p-3)) equation: 


Simplifying
400 = 4p(18 + -1(p + -3))

Reorder the terms:
400 = 4p(18 + -1(-3 + p))
400 = 4p(18 + (-3 * -1 + p * -1))
400 = 4p(18 + (3 + -1p))

Combine like terms: 18 + 3 = 21
400 = 4p(21 + -1p)
400 = (21 * 4p + -1p * 4p)
400 = (84p + -4p2)

Solving
400 = 84p + -4p2

Solving for variable 'p'.

Reorder the terms:
400 + -84p + 4p2 = 84p + -84p + -4p2 + 4p2

Combine like terms: 84p + -84p = 0
400 + -84p + 4p2 = 0 + -4p2 + 4p2
400 + -84p + 4p2 = -4p2 + 4p2

Combine like terms: -4p2 + 4p2 = 0
400 + -84p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + -21p + p2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(100 + -21p + p2)' equal to zero and attempt to solve:

Simplifying
100 + -21p + p2 = 0

Solving
100 + -21p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -21p + -100 + p2 = 0 + -100

Reorder the terms:
100 + -100 + -21p + p2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -21p + p2 = 0 + -100
-21p + p2 = 0 + -100

Combine like terms: 0 + -100 = -100
-21p + p2 = -100

The p term is -21p.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21p + 110.25 + p2 = -100 + 110.25

Reorder the terms:
110.25 + -21p + p2 = -100 + 110.25

Combine like terms: -100 + 110.25 = 10.25
110.25 + -21p + p2 = 10.25

Factor a perfect square on the left side:
(p + -10.5)(p + -10.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(p + -10.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
p + -10.5 = 3.201562119

Simplifying
p + -10.5 = 3.201562119

Reorder the terms:
-10.5 + p = 3.201562119

Solving
-10.5 + p = 3.201562119

Solving for variable 'p'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + p = 3.201562119 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + p = 3.201562119 + 10.5
p = 3.201562119 + 10.5

Combine like terms: 3.201562119 + 10.5 = 13.701562119
p = 13.701562119

Simplifying
p = 13.701562119


Subproblem 2
p + -10.5 = -3.201562119

Simplifying
p + -10.5 = -3.201562119

Reorder the terms:
-10.5 + p = -3.201562119

Solving
-10.5 + p = -3.201562119

Solving for variable 'p'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + p = -3.201562119 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + p = -3.201562119 + 10.5
p = -3.201562119 + 10.5

Combine like terms: -3.201562119 + 10.5 = 7.298437881
p = 7.298437881

Simplifying
p = 7.298437881


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {13.701562119, 7.298437881}
Solution
p = {13.701562119, 7.298437881}

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