12x^2-234x-1872=0

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Solution for 12x^2-234x-1872=0 equation: 


Simplifying
12x2 + -234x + -1872 = 0

Reorder the terms:
-1872 + -234x + 12x2 = 0

Solving
-1872 + -234x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-312 + -39x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-312 + -39x + 2x2)' equal to zero and attempt to solve:

Simplifying
-312 + -39x + 2x2 = 0

Solving
-312 + -39x + 2x2 = 0

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

Divide each side by '2'.
-156 + -19.5x + x2 = 0

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + -19.5x + 156 + x2 = 0 + 156

Reorder the terms:
-156 + 156 + -19.5x + x2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + -19.5x + x2 = 0 + 156
-19.5x + x2 = 0 + 156

Combine like terms: 0 + 156 = 156
-19.5x + x2 = 156

The x term is -19.5x.  Take half its coefficient (-9.75).
Square it (95.0625) and add it to both sides.

Add '95.0625' to each side of the equation.
-19.5x + 95.0625 + x2 = 156 + 95.0625

Reorder the terms:
95.0625 + -19.5x + x2 = 156 + 95.0625

Combine like terms: 156 + 95.0625 = 251.0625
95.0625 + -19.5x + x2 = 251.0625

Factor a perfect square on the left side:
(x + -9.75)(x + -9.75) = 251.0625

Calculate the square root of the right side: 15.844951877

Break this problem into two subproblems by setting 
(x + -9.75) equal to 15.844951877 and -15.844951877.


Subproblem 1
x + -9.75 = 15.844951877

Simplifying
x + -9.75 = 15.844951877

Reorder the terms:
-9.75 + x = 15.844951877

Solving
-9.75 + x = 15.844951877

Solving for variable 'x'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + x = 15.844951877 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + x = 15.844951877 + 9.75
x = 15.844951877 + 9.75

Combine like terms: 15.844951877 + 9.75 = 25.594951877
x = 25.594951877

Simplifying
x = 25.594951877


Subproblem 2
x + -9.75 = -15.844951877

Simplifying
x + -9.75 = -15.844951877

Reorder the terms:
-9.75 + x = -15.844951877

Solving
-9.75 + x = -15.844951877

Solving for variable 'x'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + x = -15.844951877 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + x = -15.844951877 + 9.75
x = -15.844951877 + 9.75

Combine like terms: -15.844951877 + 9.75 = -6.094951877
x = -6.094951877

Simplifying
x = -6.094951877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.594951877, -6.094951877}
Solution
x = {25.594951877, -6.094951877}

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