3x(2x+6)=12

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Solution for 3x(2x+6)=12 equation: 


Simplifying
3x(2x + 6) = 12

Reorder the terms:
3x(6 + 2x) = 12
(6 * 3x + 2x * 3x) = 12
(18x + 6x2) = 12

Solving
18x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 18x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 18x + 6x2 = 0

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

Ignore the factor 6.

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

Simplifying
-2 + 3x + x2 = 0

Solving
-2 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x + x2 = 0 + 2
3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3x + x2 = 2

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 = 2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3x + x2 = 4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 1.5 = 2.061552813

Simplifying
x + 1.5 = 2.061552813

Reorder the terms:
1.5 + x = 2.061552813

Solving
1.5 + x = 2.061552813

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 = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.061552813 + -1.5
x = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
x = 0.561552813

Simplifying
x = 0.561552813


Subproblem 2
x + 1.5 = -2.061552813

Simplifying
x + 1.5 = -2.061552813

Reorder the terms:
1.5 + x = -2.061552813

Solving
1.5 + x = -2.061552813

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 = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.061552813 + -1.5
x = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
x = -3.561552813

Simplifying
x = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.561552813, -3.561552813}
Solution
x = {0.561552813, -3.561552813}

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