(3x^2)+24x+12=0

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Solution for (3x^2)+24x+12=0 equation:


Simplifying
(3x2) + 24x + 12 = 0

Reorder the terms:
12 + 24x + (3x2) = 0

Solving
12 + 24x + (3x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 8x + x2 = 0

Solving
4 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 8x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 8x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 8x + x2 = 0 + -4
8x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
8x + x2 = -4

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -4 + 16

Reorder the terms:
16 + 8x + x2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + 8x + x2 = 12

Factor a perfect square on the left side:
(x + 4)(x + 4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 4) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + 4 = 3.464101615

Simplifying
x + 4 = 3.464101615

Reorder the terms:
4 + x = 3.464101615

Solving
4 + x = 3.464101615

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.464101615 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.464101615 + -4
x = 3.464101615 + -4

Combine like terms: 3.464101615 + -4 = -0.535898385
x = -0.535898385

Simplifying
x = -0.535898385


Subproblem 2
x + 4 = -3.464101615

Simplifying
x + 4 = -3.464101615

Reorder the terms:
4 + x = -3.464101615

Solving
4 + x = -3.464101615

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.464101615 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.464101615 + -4
x = -3.464101615 + -4

Combine like terms: -3.464101615 + -4 = -7.464101615
x = -7.464101615

Simplifying
x = -7.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.535898385, -7.464101615}
Solution
x = {-0.535898385, -7.464101615}

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