84+2x=4x(12+x)

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Solution for 84+2x=4x(12+x) equation: 


Simplifying
84 + 2x = 4x(12 + x)
84 + 2x = (12 * 4x + x * 4x)
84 + 2x = (48x + 4x2)

Solving
84 + 2x = 48x + 4x2

Solving for variable 'x'.

Combine like terms: 2x + -48x = -46x
84 + -46x + -4x2 = 48x + 4x2 + -48x + -4x2

Reorder the terms:
84 + -46x + -4x2 = 48x + -48x + 4x2 + -4x2

Combine like terms: 48x + -48x = 0
84 + -46x + -4x2 = 0 + 4x2 + -4x2
84 + -46x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
84 + -46x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -23x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(42 + -23x + -2x2)' equal to zero and attempt to solve:

Simplifying
42 + -23x + -2x2 = 0

Solving
42 + -23x + -2x2 = 0

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

Divide each side by '-2'.
-21 + 11.5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 11.5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 11.5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 11.5x + x2 = 0 + 21
11.5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
11.5x + x2 = 21

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = 21 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 21 + 33.0625

Combine like terms: 21 + 33.0625 = 54.0625
33.0625 + 11.5x + x2 = 54.0625

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 54.0625

Calculate the square root of the right side: 7.352720585

Break this problem into two subproblems by setting 
(x + 5.75) equal to 7.352720585 and -7.352720585.


Subproblem 1
x + 5.75 = 7.352720585

Simplifying
x + 5.75 = 7.352720585

Reorder the terms:
5.75 + x = 7.352720585

Solving
5.75 + x = 7.352720585

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = 7.352720585 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = 7.352720585 + -5.75
x = 7.352720585 + -5.75

Combine like terms: 7.352720585 + -5.75 = 1.602720585
x = 1.602720585

Simplifying
x = 1.602720585


Subproblem 2
x + 5.75 = -7.352720585

Simplifying
x + 5.75 = -7.352720585

Reorder the terms:
5.75 + x = -7.352720585

Solving
5.75 + x = -7.352720585

Solving for variable 'x'.

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

Add '-5.75' to each side of the equation.
5.75 + -5.75 + x = -7.352720585 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + x = -7.352720585 + -5.75
x = -7.352720585 + -5.75

Combine like terms: -7.352720585 + -5.75 = -13.102720585
x = -13.102720585

Simplifying
x = -13.102720585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.602720585, -13.102720585}
Solution
x = {1.602720585, -13.102720585}

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