15(x+6245)54x+3345=12000

Solution for 15(x+6245)54x+3345=12000 equation:

Simplifying
15(x + 6245) * 54x + 3345 = 12000

Reorder the terms:
15(6245 + x) * 54x + 3345 = 12000

Reorder the terms for easier multiplication:
15 * 54x(6245 + x) + 3345 = 12000

Multiply 15 * 54
810x(6245 + x) + 3345 = 12000
(6245 * 810x + x * 810x) + 3345 = 12000
(5058450x + 810x2) + 3345 = 12000

Reorder the terms:
3345 + 5058450x + 810x2 = 12000

Solving
3345 + 5058450x + 810x2 = 12000

Solving for variable 'x'.

Reorder the terms:
3345 + -12000 + 5058450x + 810x2 = 12000 + -12000

Combine like terms: 3345 + -12000 = -8655
-8655 + 5058450x + 810x2 = 12000 + -12000

Combine like terms: 12000 + -12000 = 0
-8655 + 5058450x + 810x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-577 + 337230x + 54x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-577 + 337230x + 54x2)' equal to zero and attempt to solve:

Simplifying
-577 + 337230x + 54x2 = 0

Solving
-577 + 337230x + 54x2 = 0

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

Divide each side by '54'.
-10.68518519 + 6245x + x2 = 0

Move the constant term to the right:

Add '10.68518519' to each side of the equation.
-10.68518519 + 6245x + 10.68518519 + x2 = 0 + 10.68518519

Reorder the terms:
-10.68518519 + 10.68518519 + 6245x + x2 = 0 + 10.68518519

Combine like terms: -10.68518519 + 10.68518519 = 0.00000000
0.00000000 + 6245x + x2 = 0 + 10.68518519
6245x + x2 = 0 + 10.68518519

Combine like terms: 0 + 10.68518519 = 10.68518519
6245x + x2 = 10.68518519

The x term is 6245x.  Take half its coefficient (3122.5).
Square it (9750006.25) and add it to both sides.

Add '9750006.25' to each side of the equation.
6245x + 9750006.25 + x2 = 10.68518519 + 9750006.25

Reorder the terms:
9750006.25 + 6245x + x2 = 10.68518519 + 9750006.25

Combine like terms: 10.68518519 + 9750006.25 = 9750016.93518519
9750006.25 + 6245x + x2 = 9750016.93518519

Factor a perfect square on the left side:
(x + 3122.5)(x + 3122.5) = 9750016.93518519

Calculate the square root of the right side: 3122.501710998

Break this problem into two subproblems by setting 
(x + 3122.5) equal to 3122.501710998 and -3122.501710998.

Subproblem 1
x + 3122.5 = 3122.501710998

Simplifying
x + 3122.5 = 3122.501710998

Reorder the terms:
3122.5 + x = 3122.501710998

Solving
3122.5 + x = 3122.501710998

Solving for variable 'x'.

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

Add '-3122.5' to each side of the equation.
3122.5 + -3122.5 + x = 3122.501710998 + -3122.5

Combine like terms: 3122.5 + -3122.5 = 0.0
0.0 + x = 3122.501710998 + -3122.5
x = 3122.501710998 + -3122.5

Combine like terms: 3122.501710998 + -3122.5 = 0.001710998
x = 0.001710998

Simplifying
x = 0.001710998

Subproblem 2
x + 3122.5 = -3122.501710998

Simplifying
x + 3122.5 = -3122.501710998

Reorder the terms:
3122.5 + x = -3122.501710998

Solving
3122.5 + x = -3122.501710998

Solving for variable 'x'.

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

Add '-3122.5' to each side of the equation.
3122.5 + -3122.5 + x = -3122.501710998 + -3122.5

Combine like terms: 3122.5 + -3122.5 = 0.0
0.0 + x = -3122.501710998 + -3122.5
x = -3122.501710998 + -3122.5

Combine like terms: -3122.501710998 + -3122.5 = -6245.001710998
x = -6245.001710998

Simplifying
x = -6245.001710998

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.001710998, -6245.001710998}
Solution
x = {0.001710998, -6245.001710998}