405-168x+12x^2=0

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Solution for 405-168x+12x^2=0 equation: 


Simplifying
405 + -168x + 12x2 = 0

Solving
405 + -168x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(135 + -56x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(135 + -56x + 4x2)' equal to zero and attempt to solve:

Simplifying
135 + -56x + 4x2 = 0

Solving
135 + -56x + 4x2 = 0

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

Divide each side by '4'.
33.75 + -14x + x2 = 0

Move the constant term to the right:

Add '-33.75' to each side of the equation.
33.75 + -14x + -33.75 + x2 = 0 + -33.75

Reorder the terms:
33.75 + -33.75 + -14x + x2 = 0 + -33.75

Combine like terms: 33.75 + -33.75 = 0.00
0.00 + -14x + x2 = 0 + -33.75
-14x + x2 = 0 + -33.75

Combine like terms: 0 + -33.75 = -33.75
-14x + x2 = -33.75

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 = -33.75 + 49

Reorder the terms:
49 + -14x + x2 = -33.75 + 49

Combine like terms: -33.75 + 49 = 15.25
49 + -14x + x2 = 15.25

Factor a perfect square on the left side:
(x + -7)(x + -7) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -7) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + -7 = 3.905124838

Simplifying
x + -7 = 3.905124838

Reorder the terms:
-7 + x = 3.905124838

Solving
-7 + x = 3.905124838

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 = 3.905124838 + 7

Combine like terms: -7 + 7 = 0
0 + x = 3.905124838 + 7
x = 3.905124838 + 7

Combine like terms: 3.905124838 + 7 = 10.905124838
x = 10.905124838

Simplifying
x = 10.905124838


Subproblem 2
x + -7 = -3.905124838

Simplifying
x + -7 = -3.905124838

Reorder the terms:
-7 + x = -3.905124838

Solving
-7 + x = -3.905124838

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 = -3.905124838 + 7

Combine like terms: -7 + 7 = 0
0 + x = -3.905124838 + 7
x = -3.905124838 + 7

Combine like terms: -3.905124838 + 7 = 3.094875162
x = 3.094875162

Simplifying
x = 3.094875162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.905124838, 3.094875162}
Solution
x = {10.905124838, 3.094875162}

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