2x(3x+3)=4

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Solution for 2x(3x+3)=4 equation: 


Simplifying
2x(3x + 3) = 4

Reorder the terms:
2x(3 + 3x) = 4
(3 * 2x + 3x * 2x) = 4
(6x + 6x2) = 4

Solving
6x + 6x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 6x + 6x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 6x + 6x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3x + 3x2 = 0

Solving
-2 + 3x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.6666666667
x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
x + x2 = 0.6666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.6666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
1.25 + x2 = 0.9166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.957427108 and -0.957427108.


Subproblem 1
x + 0.5 = 0.957427108

Simplifying
x + 0.5 = 0.957427108

Reorder the terms:
0.5 + x = 0.957427108

Solving
0.5 + x = 0.957427108

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.957427108 + -0.5
x = 0.957427108 + -0.5

Combine like terms: 0.957427108 + -0.5 = 0.457427108
x = 0.457427108

Simplifying
x = 0.457427108


Subproblem 2
x + 0.5 = -0.957427108

Simplifying
x + 0.5 = -0.957427108

Reorder the terms:
0.5 + x = -0.957427108

Solving
0.5 + x = -0.957427108

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.957427108 + -0.5
x = -0.957427108 + -0.5

Combine like terms: -0.957427108 + -0.5 = -1.457427108
x = -1.457427108

Simplifying
x = -1.457427108


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.457427108, -1.457427108}
Solution
x = {0.457427108, -1.457427108}

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