(6+x)(4x)=126

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Solution for (6+x)(4x)=126 equation: 


Simplifying
(6 + x)(4x) = 126

Remove parenthesis around (4x)
(6 + x) * 4x = 126

Reorder the terms for easier multiplication:
4x(6 + x) = 126
(6 * 4x + x * 4x) = 126
(24x + 4x2) = 126

Solving
24x + 4x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 24x + 4x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + 12x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-63 + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
-63 + 12x + 2x2 = 0

Solving
-63 + 12x + 2x2 = 0

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

Divide each side by '2'.
-31.5 + 6x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 6x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 6x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 6x + x2 = 0 + 31.5
6x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
6x + x2 = 31.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 31.5 + 9

Reorder the terms:
9 + 6x + x2 = 31.5 + 9

Combine like terms: 31.5 + 9 = 40.5
9 + 6x + x2 = 40.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 40.5

Calculate the square root of the right side: 6.363961031

Break this problem into two subproblems by setting 
(x + 3) equal to 6.363961031 and -6.363961031.


Subproblem 1
x + 3 = 6.363961031

Simplifying
x + 3 = 6.363961031

Reorder the terms:
3 + x = 6.363961031

Solving
3 + x = 6.363961031

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 6.363961031 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.363961031 + -3
x = 6.363961031 + -3

Combine like terms: 6.363961031 + -3 = 3.363961031
x = 3.363961031

Simplifying
x = 3.363961031


Subproblem 2
x + 3 = -6.363961031

Simplifying
x + 3 = -6.363961031

Reorder the terms:
3 + x = -6.363961031

Solving
3 + x = -6.363961031

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -6.363961031 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.363961031 + -3
x = -6.363961031 + -3

Combine like terms: -6.363961031 + -3 = -9.363961031
x = -9.363961031

Simplifying
x = -9.363961031


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.363961031, -9.363961031}
Solution
x = {3.363961031, -9.363961031}

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