5625=(3X+21)(3X+1)

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Solution for 5625=(3X+21)(3X+1) equation: 


Simplifying
5625 = (3X + 21)(3X + 1)

Reorder the terms:
5625 = (21 + 3X)(3X + 1)

Reorder the terms:
5625 = (21 + 3X)(1 + 3X)

Multiply (21 + 3X) * (1 + 3X)
5625 = (21(1 + 3X) + 3X * (1 + 3X))
5625 = ((1 * 21 + 3X * 21) + 3X * (1 + 3X))
5625 = ((21 + 63X) + 3X * (1 + 3X))
5625 = (21 + 63X + (1 * 3X + 3X * 3X))
5625 = (21 + 63X + (3X + 9X2))

Combine like terms: 63X + 3X = 66X
5625 = (21 + 66X + 9X2)

Solving
5625 = 21 + 66X + 9X2

Solving for variable 'X'.

Combine like terms: 5625 + -21 = 5604
5604 + -66X + -9X2 = 21 + 66X + 9X2 + -21 + -66X + -9X2

Reorder the terms:
5604 + -66X + -9X2 = 21 + -21 + 66X + -66X + 9X2 + -9X2

Combine like terms: 21 + -21 = 0
5604 + -66X + -9X2 = 0 + 66X + -66X + 9X2 + -9X2
5604 + -66X + -9X2 = 66X + -66X + 9X2 + -9X2

Combine like terms: 66X + -66X = 0
5604 + -66X + -9X2 = 0 + 9X2 + -9X2
5604 + -66X + -9X2 = 9X2 + -9X2

Combine like terms: 9X2 + -9X2 = 0
5604 + -66X + -9X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1868 + -22X + -3X2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1868 + -22X + -3X2)' equal to zero and attempt to solve:

Simplifying
1868 + -22X + -3X2 = 0

Solving
1868 + -22X + -3X2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-622.6666667 + 7.333333333X + X2 = 0

Move the constant term to the right:

Add '622.6666667' to each side of the equation.
-622.6666667 + 7.333333333X + 622.6666667 + X2 = 0 + 622.6666667

Reorder the terms:
-622.6666667 + 622.6666667 + 7.333333333X + X2 = 0 + 622.6666667

Combine like terms: -622.6666667 + 622.6666667 = 0.0000000
0.0000000 + 7.333333333X + X2 = 0 + 622.6666667
7.333333333X + X2 = 0 + 622.6666667

Combine like terms: 0 + 622.6666667 = 622.6666667
7.333333333X + X2 = 622.6666667

The X term is 7.333333333X.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333X + 13.44444445 + X2 = 622.6666667 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333X + X2 = 622.6666667 + 13.44444445

Combine like terms: 622.6666667 + 13.44444445 = 636.11111115
13.44444445 + 7.333333333X + X2 = 636.11111115

Factor a perfect square on the left side:
(X + 3.666666667)(X + 3.666666667) = 636.11111115

Calculate the square root of the right side: 25.221243251

Break this problem into two subproblems by setting 
(X + 3.666666667) equal to 25.221243251 and -25.221243251.


Subproblem 1
X + 3.666666667 = 25.221243251

Simplifying
X + 3.666666667 = 25.221243251

Reorder the terms:
3.666666667 + X = 25.221243251

Solving
3.666666667 + X = 25.221243251

Solving for variable 'X'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + X = 25.221243251 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + X = 25.221243251 + -3.666666667
X = 25.221243251 + -3.666666667

Combine like terms: 25.221243251 + -3.666666667 = 21.554576584
X = 21.554576584

Simplifying
X = 21.554576584


Subproblem 2
X + 3.666666667 = -25.221243251

Simplifying
X + 3.666666667 = -25.221243251

Reorder the terms:
3.666666667 + X = -25.221243251

Solving
3.666666667 + X = -25.221243251

Solving for variable 'X'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + X = -25.221243251 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + X = -25.221243251 + -3.666666667
X = -25.221243251 + -3.666666667

Combine like terms: -25.221243251 + -3.666666667 = -28.887909918
X = -28.887909918

Simplifying
X = -28.887909918


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {21.554576584, -28.887909918}
Solution
X = {21.554576584, -28.887909918}

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