2+3(2-x)=x(x+2)

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Solution for 2+3(2-x)=x(x+2) equation: 


Simplifying
2 + 3(2 + -1x) = x(x + 2)
2 + (2 * 3 + -1x * 3) = x(x + 2)
2 + (6 + -3x) = x(x + 2)

Combine like terms: 2 + 6 = 8
8 + -3x = x(x + 2)

Reorder the terms:
8 + -3x = x(2 + x)
8 + -3x = (2 * x + x * x)
8 + -3x = (2x + x2)

Solving
8 + -3x = 2x + x2

Solving for variable 'x'.

Combine like terms: -3x + -2x = -5x
8 + -5x + -1x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
8 + -5x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
8 + -5x + -1x2 = 0 + x2 + -1x2
8 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-8 + 5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5x + x2 = 0 + 8
5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
5x + x2 = 8

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 8 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + 5x + x2 = 14.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 2.5 = 3.774917218

Simplifying
x + 2.5 = 3.774917218

Reorder the terms:
2.5 + x = 3.774917218

Solving
2.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.774917218 + -2.5
x = 3.774917218 + -2.5

Combine like terms: 3.774917218 + -2.5 = 1.274917218
x = 1.274917218

Simplifying
x = 1.274917218


Subproblem 2
x + 2.5 = -3.774917218

Simplifying
x + 2.5 = -3.774917218

Reorder the terms:
2.5 + x = -3.774917218

Solving
2.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.774917218 + -2.5
x = -3.774917218 + -2.5

Combine like terms: -3.774917218 + -2.5 = -6.274917218
x = -6.274917218

Simplifying
x = -6.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.274917218, -6.274917218}

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