4(3x+11)=x(16+4x)

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Solution for 4(3x+11)=x(16+4x) equation: 


Simplifying
4(3x + 11) = x(16 + 4x)

Reorder the terms:
4(11 + 3x) = x(16 + 4x)
(11 * 4 + 3x * 4) = x(16 + 4x)
(44 + 12x) = x(16 + 4x)
44 + 12x = (16 * x + 4x * x)
44 + 12x = (16x + 4x2)

Solving
44 + 12x = 16x + 4x2

Solving for variable 'x'.

Combine like terms: 12x + -16x = -4x
44 + -4x + -4x2 = 16x + 4x2 + -16x + -4x2

Reorder the terms:
44 + -4x + -4x2 = 16x + -16x + 4x2 + -4x2

Combine like terms: 16x + -16x = 0
44 + -4x + -4x2 = 0 + 4x2 + -4x2
44 + -4x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
44 + -4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(11 + -1x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(11 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
11 + -1x + -1x2 = 0

Solving
11 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11 + x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x + x2 = 0 + 11
x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
x + x2 = 11

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 11 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
1.25 + x2 = 11.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 0.5 = 3.354101966

Simplifying
x + 0.5 = 3.354101966

Reorder the terms:
0.5 + x = 3.354101966

Solving
0.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.354101966 + -0.5
x = 3.354101966 + -0.5

Combine like terms: 3.354101966 + -0.5 = 2.854101966
x = 2.854101966

Simplifying
x = 2.854101966


Subproblem 2
x + 0.5 = -3.354101966

Simplifying
x + 0.5 = -3.354101966

Reorder the terms:
0.5 + x = -3.354101966

Solving
0.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.354101966 + -0.5
x = -3.354101966 + -0.5

Combine like terms: -3.354101966 + -0.5 = -3.854101966
x = -3.854101966

Simplifying
x = -3.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.854101966, -3.854101966}
Solution
x = {2.854101966, -3.854101966}

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