12x^2-9x-16x-12-6x^2-4x-21x-14-214=0

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Solution for 12x^2-9x-16x-12-6x^2-4x-21x-14-214=0 equation: 


Simplifying
12x2 + -9x + -16x + -12 + -6x2 + -4x + -21x + -14 + -214 = 0

Reorder the terms:
-12 + -14 + -214 + -9x + -16x + -4x + -21x + 12x2 + -6x2 = 0

Combine like terms: -12 + -14 = -26
-26 + -214 + -9x + -16x + -4x + -21x + 12x2 + -6x2 = 0

Combine like terms: -26 + -214 = -240
-240 + -9x + -16x + -4x + -21x + 12x2 + -6x2 = 0

Combine like terms: -9x + -16x = -25x
-240 + -25x + -4x + -21x + 12x2 + -6x2 = 0

Combine like terms: -25x + -4x = -29x
-240 + -29x + -21x + 12x2 + -6x2 = 0

Combine like terms: -29x + -21x = -50x
-240 + -50x + 12x2 + -6x2 = 0

Combine like terms: 12x2 + -6x2 = 6x2
-240 + -50x + 6x2 = 0

Solving
-240 + -50x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + -25x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-120 + -25x + 3x2)' equal to zero and attempt to solve:

Simplifying
-120 + -25x + 3x2 = 0

Solving
-120 + -25x + 3x2 = 0

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

Divide each side by '3'.
-40 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -8.333333333x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -8.333333333x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -8.333333333x + x2 = 0 + 40
-8.333333333x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-8.333333333x + x2 = 40

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = 40 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = 40 + 17.36111111

Combine like terms: 40 + 17.36111111 = 57.36111111
17.36111111 + -8.333333333x + x2 = 57.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 57.36111111

Calculate the square root of the right side: 7.573711845

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 7.573711845 and -7.573711845.


Subproblem 1
x + -4.166666667 = 7.573711845

Simplifying
x + -4.166666667 = 7.573711845

Reorder the terms:
-4.166666667 + x = 7.573711845

Solving
-4.166666667 + x = 7.573711845

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 7.573711845 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 7.573711845 + 4.166666667
x = 7.573711845 + 4.166666667

Combine like terms: 7.573711845 + 4.166666667 = 11.740378512
x = 11.740378512

Simplifying
x = 11.740378512


Subproblem 2
x + -4.166666667 = -7.573711845

Simplifying
x + -4.166666667 = -7.573711845

Reorder the terms:
-4.166666667 + x = -7.573711845

Solving
-4.166666667 + x = -7.573711845

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -7.573711845 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -7.573711845 + 4.166666667
x = -7.573711845 + 4.166666667

Combine like terms: -7.573711845 + 4.166666667 = -3.407045178
x = -3.407045178

Simplifying
x = -3.407045178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.740378512, -3.407045178}
Solution
x = {11.740378512, -3.407045178}

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