3x(2x+4)=12

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Solution for 3x(2x+4)=12 equation:


Simplifying
3x(2x + 4) = 12

Reorder the terms:
3x(4 + 2x) = 12
(4 * 3x + 2x * 3x) = 12
(12x + 6x2) = 12

Solving
12x + 6x2 = 12

Solving for variable 'x'.

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

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

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

Ignore the factor 6.

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

Simplifying
-2 + 2x + x2 = 0

Solving
-2 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 2 + 1

Reorder the terms:
1 + 2x + x2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2x + x2 = 3

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 1) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 1 = 1.732050808

Simplifying
x + 1 = 1.732050808

Reorder the terms:
1 + x = 1.732050808

Solving
1 + x = 1.732050808

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.732050808 + -1
x = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
x = 0.732050808

Simplifying
x = 0.732050808


Subproblem 2
x + 1 = -1.732050808

Simplifying
x + 1 = -1.732050808

Reorder the terms:
1 + x = -1.732050808

Solving
1 + x = -1.732050808

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.732050808 + -1
x = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
x = -2.732050808

Simplifying
x = -2.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.732050808, -2.732050808}
Solution
x = {0.732050808, -2.732050808}

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