6x-12=-54x^2+27x

Solution for 6x-12=-54x^2+27x equation:

Simplifying
6x + -12 = -54x2 + 27x

Reorder the terms:
-12 + 6x = -54x2 + 27x

Reorder the terms:
-12 + 6x = 27x + -54x2

Solving
-12 + 6x = 27x + -54x2

Solving for variable 'x'.

Combine like terms: 6x + -27x = -21x
-12 + -21x + 54x2 = 27x + -54x2 + -27x + 54x2

Reorder the terms:
-12 + -21x + 54x2 = 27x + -27x + -54x2 + 54x2

Combine like terms: 27x + -27x = 0
-12 + -21x + 54x2 = 0 + -54x2 + 54x2
-12 + -21x + 54x2 = -54x2 + 54x2

Combine like terms: -54x2 + 54x2 = 0
-12 + -21x + 54x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -7x + 18x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -7x + 18x2)' equal to zero and attempt to solve:

Simplifying
-4 + -7x + 18x2 = 0

Solving
-4 + -7x + 18x2 = 0

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

Divide each side by '18'.
-0.2222222222 + -0.3888888889x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.3888888889x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.3888888889x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.3888888889x + x2 = 0 + 0.2222222222
-0.3888888889x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.3888888889x + x2 = 0.2222222222

The x term is -0.3888888889x.  Take half its coefficient (-0.1944444445).
Square it (0.03780864200) and add it to both sides.

Add '0.03780864200' to each side of the equation.
-0.3888888889x + 0.03780864200 + x2 = 0.2222222222 + 0.03780864200

Reorder the terms:
0.03780864200 + -0.3888888889x + x2 = 0.2222222222 + 0.03780864200

Combine like terms: 0.2222222222 + 0.03780864200 = 0.2600308642
0.03780864200 + -0.3888888889x + x2 = 0.2600308642

Factor a perfect square on the left side:
(x + -0.1944444445)(x + -0.1944444445) = 0.2600308642

Calculate the square root of the right side: 0.509932215

Break this problem into two subproblems by setting 
(x + -0.1944444445) equal to 0.509932215 and -0.509932215.

Subproblem 1
x + -0.1944444445 = 0.509932215

Simplifying
x + -0.1944444445 = 0.509932215

Reorder the terms:
-0.1944444445 + x = 0.509932215

Solving
-0.1944444445 + x = 0.509932215

Solving for variable 'x'.

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

Add '0.1944444445' to each side of the equation.
-0.1944444445 + 0.1944444445 + x = 0.509932215 + 0.1944444445

Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000
0.0000000000 + x = 0.509932215 + 0.1944444445
x = 0.509932215 + 0.1944444445

Combine like terms: 0.509932215 + 0.1944444445 = 0.7043766595
x = 0.7043766595

Simplifying
x = 0.7043766595

Subproblem 2
x + -0.1944444445 = -0.509932215

Simplifying
x + -0.1944444445 = -0.509932215

Reorder the terms:
-0.1944444445 + x = -0.509932215

Solving
-0.1944444445 + x = -0.509932215

Solving for variable 'x'.

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

Add '0.1944444445' to each side of the equation.
-0.1944444445 + 0.1944444445 + x = -0.509932215 + 0.1944444445

Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000
0.0000000000 + x = -0.509932215 + 0.1944444445
x = -0.509932215 + 0.1944444445

Combine like terms: -0.509932215 + 0.1944444445 = -0.3154877705
x = -0.3154877705

Simplifying
x = -0.3154877705

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7043766595, -0.3154877705}
Solution
x = {0.7043766595, -0.3154877705}