3x(4x+12)=3

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Solution for 3x(4x+12)=3 equation: 


Simplifying
3x(4x + 12) = 3

Reorder the terms:
3x(12 + 4x) = 3
(12 * 3x + 4x * 3x) = 3
(36x + 12x2) = 3

Solving
36x + 12x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 36x + 12x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 12x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 12x + 4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + 4x2 = 0

Solving
-1 + 12x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 3x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 3x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 3x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 3x + x2 = 0 + 0.25
3x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
3x + x2 = 0.25

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 = 0.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.25 + 2.25

Combine like terms: 0.25 + 2.25 = 2.5
2.25 + 3x + x2 = 2.5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.58113883 and -1.58113883.


Subproblem 1
x + 1.5 = 1.58113883

Simplifying
x + 1.5 = 1.58113883

Reorder the terms:
1.5 + x = 1.58113883

Solving
1.5 + x = 1.58113883

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 = 1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.58113883 + -1.5
x = 1.58113883 + -1.5

Combine like terms: 1.58113883 + -1.5 = 0.08113883
x = 0.08113883

Simplifying
x = 0.08113883


Subproblem 2
x + 1.5 = -1.58113883

Simplifying
x + 1.5 = -1.58113883

Reorder the terms:
1.5 + x = -1.58113883

Solving
1.5 + x = -1.58113883

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 = -1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.58113883 + -1.5
x = -1.58113883 + -1.5

Combine like terms: -1.58113883 + -1.5 = -3.08113883
x = -3.08113883

Simplifying
x = -3.08113883


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.08113883, -3.08113883}
Solution
x = {0.08113883, -3.08113883}

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