(-84-3x+(6x*6x))=0

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Solution for (-84-3x+(6x*6x))=0 equation: 


Simplifying
(-84 + -3x + (6x * 6x)) = 0

Reorder the terms for easier multiplication:
(-84 + -3x + (6 * 6x * x)) = 0

Multiply 6 * 6
(-84 + -3x + (36x * x)) = 0

Multiply x * x
(-84 + -3x + (36x2)) = 0

Remove parenthesis around (-84 + -3x + (36x2))
-84 + -3x + (36x2) = 0

Solving
-84 + -3x + (36x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -1x + (12x2)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-28 + -1x + (12x2))' equal to zero and attempt to solve:

Simplifying
-28 + -1x + (12x2) = 0

Solving
-28 + -1x + (12x2) = 0

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

Divide each side by '12'.
-2.333333333 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -0.08333333333x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -0.08333333333x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -0.08333333333x + x2 = 0 + 2.333333333
-0.08333333333x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-0.08333333333x + x2 = 2.333333333

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 2.333333333 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 2.333333333 + 0.001736111111

Combine like terms: 2.333333333 + 0.001736111111 = 2.335069444111
0.001736111111 + -0.08333333333x + x2 = 2.335069444111

Factor a perfect square on the left side:
((x) + -0.04166666667)((x) + -0.04166666667) = 2.335069444111

Calculate the square root of the right side: 1.528093402

Break this problem into two subproblems by setting 
((x) + -0.04166666667) equal to 1.528093402 and -1.528093402.


Subproblem 1
(x) + -0.04166666667 = 1.528093402

Simplifying
(x) + -0.04166666667 = 1.528093402
x + -0.04166666667 = 1.528093402

Reorder the terms:
-0.04166666667 + x = 1.528093402

Solving
-0.04166666667 + x = 1.528093402

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 1.528093402 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 1.528093402 + 0.04166666667
x = 1.528093402 + 0.04166666667

Combine like terms: 1.528093402 + 0.04166666667 = 1.56976006867
x = 1.56976006867

Simplifying
x = 1.56976006867


Subproblem 2
(x) + -0.04166666667 = -1.528093402

Simplifying
(x) + -0.04166666667 = -1.528093402
x + -0.04166666667 = -1.528093402

Reorder the terms:
-0.04166666667 + x = -1.528093402

Solving
-0.04166666667 + x = -1.528093402

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -1.528093402 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -1.528093402 + 0.04166666667
x = -1.528093402 + 0.04166666667

Combine like terms: -1.528093402 + 0.04166666667 = -1.48642673533
x = -1.48642673533

Simplifying
x = -1.48642673533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.56976006867, -1.48642673533}
Solution
x = {1.56976006867, -1.48642673533}

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