3x^2-108x-2187=0

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Solution for 3x^2-108x-2187=0 equation: 


Simplifying
3x2 + -108x + -2187 = 0

Reorder the terms:
-2187 + -108x + 3x2 = 0

Solving
-2187 + -108x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-729 + -36x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-729 + -36x + x2)' equal to zero and attempt to solve:

Simplifying
-729 + -36x + x2 = 0

Solving
-729 + -36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '729' to each side of the equation.
-729 + -36x + 729 + x2 = 0 + 729

Reorder the terms:
-729 + 729 + -36x + x2 = 0 + 729

Combine like terms: -729 + 729 = 0
0 + -36x + x2 = 0 + 729
-36x + x2 = 0 + 729

Combine like terms: 0 + 729 = 729
-36x + x2 = 729

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = 729 + 324

Reorder the terms:
324 + -36x + x2 = 729 + 324

Combine like terms: 729 + 324 = 1053
324 + -36x + x2 = 1053

Factor a perfect square on the left side:
(x + -18)(x + -18) = 1053

Calculate the square root of the right side: 32.449961479

Break this problem into two subproblems by setting 
(x + -18) equal to 32.449961479 and -32.449961479.


Subproblem 1
x + -18 = 32.449961479

Simplifying
x + -18 = 32.449961479

Reorder the terms:
-18 + x = 32.449961479

Solving
-18 + x = 32.449961479

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = 32.449961479 + 18

Combine like terms: -18 + 18 = 0
0 + x = 32.449961479 + 18
x = 32.449961479 + 18

Combine like terms: 32.449961479 + 18 = 50.449961479
x = 50.449961479

Simplifying
x = 50.449961479


Subproblem 2
x + -18 = -32.449961479

Simplifying
x + -18 = -32.449961479

Reorder the terms:
-18 + x = -32.449961479

Solving
-18 + x = -32.449961479

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = -32.449961479 + 18

Combine like terms: -18 + 18 = 0
0 + x = -32.449961479 + 18
x = -32.449961479 + 18

Combine like terms: -32.449961479 + 18 = -14.449961479
x = -14.449961479

Simplifying
x = -14.449961479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.449961479, -14.449961479}
Solution
x = {50.449961479, -14.449961479}

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