6x-27x+72=3x(2x+3)

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Solution for 6x-27x+72=3x(2x+3) equation: 


Simplifying
6x + -27x + 72 = 3x(2x + 3)

Reorder the terms:
72 + 6x + -27x = 3x(2x + 3)

Combine like terms: 6x + -27x = -21x
72 + -21x = 3x(2x + 3)

Reorder the terms:
72 + -21x = 3x(3 + 2x)
72 + -21x = (3 * 3x + 2x * 3x)
72 + -21x = (9x + 6x2)

Solving
72 + -21x = 9x + 6x2

Solving for variable 'x'.

Combine like terms: -21x + -9x = -30x
72 + -30x + -6x2 = 9x + 6x2 + -9x + -6x2

Reorder the terms:
72 + -30x + -6x2 = 9x + -9x + 6x2 + -6x2

Combine like terms: 9x + -9x = 0
72 + -30x + -6x2 = 0 + 6x2 + -6x2
72 + -30x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
72 + -30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -5x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(12 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -5x + -1x2 = 0

Solving
12 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-12 + 5x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 5x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 5x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 5x + x2 = 0 + 12
5x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
5x + x2 = 12

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 = 12 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 12 + 6.25

Combine like terms: 12 + 6.25 = 18.25
6.25 + 5x + x2 = 18.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 2.5 = 4.272001873

Simplifying
x + 2.5 = 4.272001873

Reorder the terms:
2.5 + x = 4.272001873

Solving
2.5 + x = 4.272001873

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 = 4.272001873 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.272001873 + -2.5
x = 4.272001873 + -2.5

Combine like terms: 4.272001873 + -2.5 = 1.772001873
x = 1.772001873

Simplifying
x = 1.772001873


Subproblem 2
x + 2.5 = -4.272001873

Simplifying
x + 2.5 = -4.272001873

Reorder the terms:
2.5 + x = -4.272001873

Solving
2.5 + x = -4.272001873

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 = -4.272001873 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.272001873 + -2.5
x = -4.272001873 + -2.5

Combine like terms: -4.272001873 + -2.5 = -6.772001873
x = -6.772001873

Simplifying
x = -6.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.772001873, -6.772001873}
Solution
x = {1.772001873, -6.772001873}

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