2x(3x-9)=39

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Solution for 2x(3x-9)=39 equation: 


Simplifying
2x(3x + -9) = 39

Reorder the terms:
2x(-9 + 3x) = 39
(-9 * 2x + 3x * 2x) = 39
(-18x + 6x2) = 39

Solving
-18x + 6x2 = 39

Solving for variable 'x'.

Reorder the terms:
-39 + -18x + 6x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + -18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + -6x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-13 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-13 + -6x + 2x2 = 0

Solving
-13 + -6x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + -3x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -3x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -3x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -3x + x2 = 0 + 6.5
-3x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-3x + x2 = 6.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 6.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 6.5 + 2.25

Combine like terms: 6.5 + 2.25 = 8.75
2.25 + -3x + x2 = 8.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
x + -1.5 = 2.958039892

Simplifying
x + -1.5 = 2.958039892

Reorder the terms:
-1.5 + x = 2.958039892

Solving
-1.5 + x = 2.958039892

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.958039892 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.958039892 + 1.5
x = 2.958039892 + 1.5

Combine like terms: 2.958039892 + 1.5 = 4.458039892
x = 4.458039892

Simplifying
x = 4.458039892


Subproblem 2
x + -1.5 = -2.958039892

Simplifying
x + -1.5 = -2.958039892

Reorder the terms:
-1.5 + x = -2.958039892

Solving
-1.5 + x = -2.958039892

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.958039892 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.958039892 + 1.5
x = -2.958039892 + 1.5

Combine like terms: -2.958039892 + 1.5 = -1.458039892
x = -1.458039892

Simplifying
x = -1.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.458039892, -1.458039892}
Solution
x = {4.458039892, -1.458039892}

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