(12+2X)(7+2X)=140

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Solution for (12+2X)(7+2X)=140 equation: 


Simplifying
(12 + 2X)(7 + 2X) = 140

Multiply (12 + 2X) * (7 + 2X)
(12(7 + 2X) + 2X * (7 + 2X)) = 140
((7 * 12 + 2X * 12) + 2X * (7 + 2X)) = 140
((84 + 24X) + 2X * (7 + 2X)) = 140
(84 + 24X + (7 * 2X + 2X * 2X)) = 140
(84 + 24X + (14X + 4X2)) = 140

Combine like terms: 24X + 14X = 38X
(84 + 38X + 4X2) = 140

Solving
84 + 38X + 4X2 = 140

Solving for variable 'X'.

Reorder the terms:
84 + -140 + 38X + 4X2 = 140 + -140

Combine like terms: 84 + -140 = -56
-56 + 38X + 4X2 = 140 + -140

Combine like terms: 140 + -140 = 0
-56 + 38X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 19X + 2X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + 19X + 2X2)' equal to zero and attempt to solve:

Simplifying
-28 + 19X + 2X2 = 0

Solving
-28 + 19X + 2X2 = 0

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

Divide each side by '2'.
-14 + 9.5X + X2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 9.5X + 14 + X2 = 0 + 14

Reorder the terms:
-14 + 14 + 9.5X + X2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 9.5X + X2 = 0 + 14
9.5X + X2 = 0 + 14

Combine like terms: 0 + 14 = 14
9.5X + X2 = 14

The X term is 9.5X.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5X + 22.5625 + X2 = 14 + 22.5625

Reorder the terms:
22.5625 + 9.5X + X2 = 14 + 22.5625

Combine like terms: 14 + 22.5625 = 36.5625
22.5625 + 9.5X + X2 = 36.5625

Factor a perfect square on the left side:
(X + 4.75)(X + 4.75) = 36.5625

Calculate the square root of the right side: 6.046693311

Break this problem into two subproblems by setting 
(X + 4.75) equal to 6.046693311 and -6.046693311.


Subproblem 1
X + 4.75 = 6.046693311

Simplifying
X + 4.75 = 6.046693311

Reorder the terms:
4.75 + X = 6.046693311

Solving
4.75 + X = 6.046693311

Solving for variable 'X'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + X = 6.046693311 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + X = 6.046693311 + -4.75
X = 6.046693311 + -4.75

Combine like terms: 6.046693311 + -4.75 = 1.296693311
X = 1.296693311

Simplifying
X = 1.296693311


Subproblem 2
X + 4.75 = -6.046693311

Simplifying
X + 4.75 = -6.046693311

Reorder the terms:
4.75 + X = -6.046693311

Solving
4.75 + X = -6.046693311

Solving for variable 'X'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + X = -6.046693311 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + X = -6.046693311 + -4.75
X = -6.046693311 + -4.75

Combine like terms: -6.046693311 + -4.75 = -10.796693311
X = -10.796693311

Simplifying
X = -10.796693311


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.296693311, -10.796693311}
Solution
X = {1.296693311, -10.796693311}

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