4x(9-3x)=2

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Solution for 4x(9-3x)=2 equation: 


Simplifying
4x(9 + -3x) = 2
(9 * 4x + -3x * 4x) = 2
(36x + -12x2) = 2

Solving
36x + -12x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 36x + -12x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 36x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 18x + -6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 18x + -6x2)' equal to zero and attempt to solve:

Simplifying
-1 + 18x + -6x2 = 0

Solving
-1 + 18x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.1666666667 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -3x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -3x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + -0.1666666667
-3x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-3x + x2 = -0.1666666667

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 = -0.1666666667 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.1666666667 + 2.25

Combine like terms: -0.1666666667 + 2.25 = 2.0833333333
2.25 + -3x + x2 = 2.0833333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.0833333333

Calculate the square root of the right side: 1.443375673

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.443375673 and -1.443375673.


Subproblem 1
x + -1.5 = 1.443375673

Simplifying
x + -1.5 = 1.443375673

Reorder the terms:
-1.5 + x = 1.443375673

Solving
-1.5 + x = 1.443375673

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 = 1.443375673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.443375673 + 1.5
x = 1.443375673 + 1.5

Combine like terms: 1.443375673 + 1.5 = 2.943375673
x = 2.943375673

Simplifying
x = 2.943375673


Subproblem 2
x + -1.5 = -1.443375673

Simplifying
x + -1.5 = -1.443375673

Reorder the terms:
-1.5 + x = -1.443375673

Solving
-1.5 + x = -1.443375673

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 = -1.443375673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.443375673 + 1.5
x = -1.443375673 + 1.5

Combine like terms: -1.443375673 + 1.5 = 0.056624327
x = 0.056624327

Simplifying
x = 0.056624327


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.943375673, 0.056624327}
Solution
x = {2.943375673, 0.056624327}

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