6x^2-84x-12=0

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Solution for 6x^2-84x-12=0 equation: 


Simplifying
6x2 + -84x + -12 = 0

Reorder the terms:
-12 + -84x + 6x2 = 0

Solving
-12 + -84x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -14x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-2 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -14x + x2 = 0

Solving
-2 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -14x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -14x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -14x + x2 = 0 + 2
-14x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-14x + x2 = 2

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 2 + 49

Reorder the terms:
49 + -14x + x2 = 2 + 49

Combine like terms: 2 + 49 = 51
49 + -14x + x2 = 51

Factor a perfect square on the left side:
(x + -7)(x + -7) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -7) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + -7 = 7.141428429

Simplifying
x + -7 = 7.141428429

Reorder the terms:
-7 + x = 7.141428429

Solving
-7 + x = 7.141428429

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 7.141428429 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.141428429 + 7
x = 7.141428429 + 7

Combine like terms: 7.141428429 + 7 = 14.141428429
x = 14.141428429

Simplifying
x = 14.141428429


Subproblem 2
x + -7 = -7.141428429

Simplifying
x + -7 = -7.141428429

Reorder the terms:
-7 + x = -7.141428429

Solving
-7 + x = -7.141428429

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -7.141428429 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.141428429 + 7
x = -7.141428429 + 7

Combine like terms: -7.141428429 + 7 = -0.141428429
x = -0.141428429

Simplifying
x = -0.141428429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.141428429, -0.141428429}
Solution
x = {14.141428429, -0.141428429}

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