3x(x+6)=2(x-3)+4x

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Solution for 3x(x+6)=2(x-3)+4x equation:


Simplifying
3x(x + 6) = 2(x + -3) + 4x

Reorder the terms:
3x(6 + x) = 2(x + -3) + 4x
(6 * 3x + x * 3x) = 2(x + -3) + 4x
(18x + 3x2) = 2(x + -3) + 4x

Reorder the terms:
18x + 3x2 = 2(-3 + x) + 4x
18x + 3x2 = (-3 * 2 + x * 2) + 4x
18x + 3x2 = (-6 + 2x) + 4x

Combine like terms: 2x + 4x = 6x
18x + 3x2 = -6 + 6x

Solving
18x + 3x2 = -6 + 6x

Solving for variable 'x'.

Reorder the terms:
6 + 18x + -6x + 3x2 = -6 + 6x + 6 + -6x

Combine like terms: 18x + -6x = 12x
6 + 12x + 3x2 = -6 + 6x + 6 + -6x

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

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

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

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 2) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 2 = 1.414213562

Simplifying
x + 2 = 1.414213562

Reorder the terms:
2 + x = 1.414213562

Solving
2 + x = 1.414213562

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 = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.414213562 + -2
x = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
x = -0.585786438

Simplifying
x = -0.585786438


Subproblem 2
x + 2 = -1.414213562

Simplifying
x + 2 = -1.414213562

Reorder the terms:
2 + x = -1.414213562

Solving
2 + x = -1.414213562

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 = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.414213562 + -2
x = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
x = -3.414213562

Simplifying
x = -3.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.585786438, -3.414213562}
Solution
x = {-0.585786438, -3.414213562}

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