0=108-84x+12x^2

Solution for 0=108-84x+12x^2 equation:

Simplifying
0 = 108 + -84x + 12x2

Solving
0 = 108 + -84x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -108 = -108
-108 + 84x + -12x2 = 108 + -84x + 12x2 + -108 + 84x + -12x2

Reorder the terms:
-108 + 84x + -12x2 = 108 + -108 + -84x + 84x + 12x2 + -12x2

Combine like terms: 108 + -108 = 0
-108 + 84x + -12x2 = 0 + -84x + 84x + 12x2 + -12x2
-108 + 84x + -12x2 = -84x + 84x + 12x2 + -12x2

Combine like terms: -84x + 84x = 0
-108 + 84x + -12x2 = 0 + 12x2 + -12x2
-108 + 84x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-108 + 84x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-9 + 7x + -1x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-9 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
-9 + 7x + -1x2 = 0

Solving
-9 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
9 + -7x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -7x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -7x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x + x2 = 0 + -9
-7x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-7x + x2 = -9

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -9 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -9 + 12.25

Combine like terms: -9 + 12.25 = 3.25
12.25 + -7x + x2 = 3.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -3.5 = 1.802775638

Simplifying
x + -3.5 = 1.802775638

Reorder the terms:
-3.5 + x = 1.802775638

Solving
-3.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 1.802775638 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 1.802775638 + 3.5
x = 1.802775638 + 3.5

Combine like terms: 1.802775638 + 3.5 = 5.302775638
x = 5.302775638

Simplifying
x = 5.302775638

Subproblem 2
x + -3.5 = -1.802775638

Simplifying
x + -3.5 = -1.802775638

Reorder the terms:
-3.5 + x = -1.802775638

Solving
-3.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -1.802775638 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -1.802775638 + 3.5
x = -1.802775638 + 3.5

Combine like terms: -1.802775638 + 3.5 = 1.697224362
x = 1.697224362

Simplifying
x = 1.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.302775638, 1.697224362}
Solution
x = {5.302775638, 1.697224362}