12x^2+96x+80=0

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Solution for 12x^2+96x+80=0 equation: 


Simplifying
12x2 + 96x + 80 = 0

Reorder the terms:
80 + 96x + 12x2 = 0

Solving
80 + 96x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 24x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + 24x + 3x2 = 0

Solving
20 + 24x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
6.666666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + 8x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + 8x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + 8x + x2 = 0 + -6.666666667
8x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
8x + x2 = -6.666666667

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 = -6.666666667 + 16

Reorder the terms:
16 + 8x + x2 = -6.666666667 + 16

Combine like terms: -6.666666667 + 16 = 9.333333333
16 + 8x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + 4) equal to 3.055050463 and -3.055050463.


Subproblem 1
x + 4 = 3.055050463

Simplifying
x + 4 = 3.055050463

Reorder the terms:
4 + x = 3.055050463

Solving
4 + x = 3.055050463

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 = 3.055050463 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.055050463 + -4
x = 3.055050463 + -4

Combine like terms: 3.055050463 + -4 = -0.944949537
x = -0.944949537

Simplifying
x = -0.944949537


Subproblem 2
x + 4 = -3.055050463

Simplifying
x + 4 = -3.055050463

Reorder the terms:
4 + x = -3.055050463

Solving
4 + x = -3.055050463

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 = -3.055050463 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.055050463 + -4
x = -3.055050463 + -4

Combine like terms: -3.055050463 + -4 = -7.055050463
x = -7.055050463

Simplifying
x = -7.055050463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.944949537, -7.055050463}
Solution
x = {-0.944949537, -7.055050463}

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