2x(x+3)=12

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

Simplifying
2x(x + 3) = 12

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

Solving
6x + 2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 6x + 2x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + 3x + x2 = 0

Solving
-6 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3x + x2 = 0 + 6
3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3x + x2 = 6

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 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3x + x2 = 8.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 1.5 = 2.872281323

Simplifying
x + 1.5 = 2.872281323

Reorder the terms:
1.5 + x = 2.872281323

Solving
1.5 + x = 2.872281323

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 = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.872281323 + -1.5
x = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
x = 1.372281323

Simplifying
x = 1.372281323

Subproblem 2
x + 1.5 = -2.872281323

Simplifying
x + 1.5 = -2.872281323

Reorder the terms:
1.5 + x = -2.872281323

Solving
1.5 + x = -2.872281323

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 = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.872281323 + -1.5
x = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
x = -4.372281323

Simplifying
x = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.372281323, -4.372281323}
Solution
x = {1.372281323, -4.372281323}