3(x+4)x=6

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Solution for 3(x+4)x=6 equation: 


Simplifying
3(x + 4) * x = 6

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

Reorder the terms for easier multiplication:
3x(4 + x) = 6
(4 * 3x + x * 3x) = 6
(12x + 3x2) = 6

Solving
12x + 3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + 3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 4x + x2 = 0

Solving
-2 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4x + x2 = 0 + 2
4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4x + x2 = 2

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 2 + 4

Reorder the terms:
4 + 4x + x2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4x + x2 = 6

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 2 = 2.449489743

Simplifying
x + 2 = 2.449489743

Reorder the terms:
2 + x = 2.449489743

Solving
2 + x = 2.449489743

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.449489743 + -2
x = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
x = 0.449489743

Simplifying
x = 0.449489743


Subproblem 2
x + 2 = -2.449489743

Simplifying
x + 2 = -2.449489743

Reorder the terms:
2 + x = -2.449489743

Solving
2 + x = -2.449489743

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.449489743 + -2
x = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
x = -4.449489743

Simplifying
x = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.449489743, -4.449489743}
Solution
x = {0.449489743, -4.449489743}

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