3(-4+4x+x^2)=0

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Solution for 3(-4+4x+x^2)=0 equation: 


Simplifying
3(-4 + 4x + x2) = 0
(-4 * 3 + 4x * 3 + x2 * 3) = 0
(-12 + 12x + 3x2) = 0

Solving
-12 + 12x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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

Simplifying
-4 + 4x + x2 = 0

Solving
-4 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

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

Factor a perfect square on the left side:
(x + 2)(x + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 2 = 2.828427125

Simplifying
x + 2 = 2.828427125

Reorder the terms:
2 + x = 2.828427125

Solving
2 + x = 2.828427125

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 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.828427125 + -2
x = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
x = 0.828427125

Simplifying
x = 0.828427125


Subproblem 2
x + 2 = -2.828427125

Simplifying
x + 2 = -2.828427125

Reorder the terms:
2 + x = -2.828427125

Solving
2 + x = -2.828427125

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 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.828427125 + -2
x = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
x = -4.828427125

Simplifying
x = -4.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.828427125, -4.828427125}
Solution
x = {0.828427125, -4.828427125}

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