(x+6)(2x+4)=420

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Solution for (x+6)(2x+4)=420 equation: 


Simplifying
(x + 6)(2x + 4) = 420

Reorder the terms:
(6 + x)(2x + 4) = 420

Reorder the terms:
(6 + x)(4 + 2x) = 420

Multiply (6 + x) * (4 + 2x)
(6(4 + 2x) + x(4 + 2x)) = 420
((4 * 6 + 2x * 6) + x(4 + 2x)) = 420
((24 + 12x) + x(4 + 2x)) = 420
(24 + 12x + (4 * x + 2x * x)) = 420
(24 + 12x + (4x + 2x2)) = 420

Combine like terms: 12x + 4x = 16x
(24 + 16x + 2x2) = 420

Solving
24 + 16x + 2x2 = 420

Solving for variable 'x'.

Reorder the terms:
24 + -420 + 16x + 2x2 = 420 + -420

Combine like terms: 24 + -420 = -396
-396 + 16x + 2x2 = 420 + -420

Combine like terms: 420 + -420 = 0
-396 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-198 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-198 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-198 + 8x + x2 = 0

Solving
-198 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '198' to each side of the equation.
-198 + 8x + 198 + x2 = 0 + 198

Reorder the terms:
-198 + 198 + 8x + x2 = 0 + 198

Combine like terms: -198 + 198 = 0
0 + 8x + x2 = 0 + 198
8x + x2 = 0 + 198

Combine like terms: 0 + 198 = 198
8x + x2 = 198

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 198 + 16

Reorder the terms:
16 + 8x + x2 = 198 + 16

Combine like terms: 198 + 16 = 214
16 + 8x + x2 = 214

Factor a perfect square on the left side:
(x + 4)(x + 4) = 214

Calculate the square root of the right side: 14.628738838

Break this problem into two subproblems by setting 
(x + 4) equal to 14.628738838 and -14.628738838.


Subproblem 1
x + 4 = 14.628738838

Simplifying
x + 4 = 14.628738838

Reorder the terms:
4 + x = 14.628738838

Solving
4 + x = 14.628738838

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 14.628738838 + -4

Combine like terms: 4 + -4 = 0
0 + x = 14.628738838 + -4
x = 14.628738838 + -4

Combine like terms: 14.628738838 + -4 = 10.628738838
x = 10.628738838

Simplifying
x = 10.628738838


Subproblem 2
x + 4 = -14.628738838

Simplifying
x + 4 = -14.628738838

Reorder the terms:
4 + x = -14.628738838

Solving
4 + x = -14.628738838

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -14.628738838 + -4

Combine like terms: 4 + -4 = 0
0 + x = -14.628738838 + -4
x = -14.628738838 + -4

Combine like terms: -14.628738838 + -4 = -18.628738838
x = -18.628738838

Simplifying
x = -18.628738838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.628738838, -18.628738838}
Solution
x = {10.628738838, -18.628738838}

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