(2x+8)(x+6)=84

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Solution for (2x+8)(x+6)=84 equation: 


Simplifying
(2x + 8)(x + 6) = 84

Reorder the terms:
(8 + 2x)(x + 6) = 84

Reorder the terms:
(8 + 2x)(6 + x) = 84

Multiply (8 + 2x) * (6 + x)
(8(6 + x) + 2x * (6 + x)) = 84
((6 * 8 + x * 8) + 2x * (6 + x)) = 84
((48 + 8x) + 2x * (6 + x)) = 84
(48 + 8x + (6 * 2x + x * 2x)) = 84
(48 + 8x + (12x + 2x2)) = 84

Combine like terms: 8x + 12x = 20x
(48 + 20x + 2x2) = 84

Solving
48 + 20x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
48 + -84 + 20x + 2x2 = 84 + -84

Combine like terms: 48 + -84 = -36
-36 + 20x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-36 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + 10x + x2 = 0

Solving
-18 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 10x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 10x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 10x + x2 = 0 + 18
10x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
10x + x2 = 18

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 18 + 25

Reorder the terms:
25 + 10x + x2 = 18 + 25

Combine like terms: 18 + 25 = 43
25 + 10x + x2 = 43

Factor a perfect square on the left side:
(x + 5)(x + 5) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + 5) equal to 6.557438524 and -6.557438524.


Subproblem 1
x + 5 = 6.557438524

Simplifying
x + 5 = 6.557438524

Reorder the terms:
5 + x = 6.557438524

Solving
5 + x = 6.557438524

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.557438524 + -5
x = 6.557438524 + -5

Combine like terms: 6.557438524 + -5 = 1.557438524
x = 1.557438524

Simplifying
x = 1.557438524


Subproblem 2
x + 5 = -6.557438524

Simplifying
x + 5 = -6.557438524

Reorder the terms:
5 + x = -6.557438524

Solving
5 + x = -6.557438524

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.557438524 + -5
x = -6.557438524 + -5

Combine like terms: -6.557438524 + -5 = -11.557438524
x = -11.557438524

Simplifying
x = -11.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.557438524, -11.557438524}
Solution
x = {1.557438524, -11.557438524}

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