27x^2-12x-4=8

Solution for 27x^2-12x-4=8 equation:

Simplifying
27x2 + -12x + -4 = 8

Reorder the terms:
-4 + -12x + 27x2 = 8

Solving
-4 + -12x + 27x2 = 8

Solving for variable 'x'.

Reorder the terms:
-4 + -8 + -12x + 27x2 = 8 + -8

Combine like terms: -4 + -8 = -12
-12 + -12x + 27x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-12 + -12x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -4x + 9x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -4x + 9x2)' equal to zero and attempt to solve:

Simplifying
-4 + -4x + 9x2 = 0

Solving
-4 + -4x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.4444444444x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.4444444444x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.4444444444x + x2 = 0 + 0.4444444444
-0.4444444444x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.4444444444x + x2 = 0.4444444444

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 0.4444444444 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 0.4444444444 + 0.04938271604

Combine like terms: 0.4444444444 + 0.04938271604 = 0.49382716044
0.04938271604 + -0.4444444444x + x2 = 0.49382716044

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.49382716044

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.702728369 and -0.702728369.

Subproblem 1
x + -0.2222222222 = 0.702728369

Simplifying
x + -0.2222222222 = 0.702728369

Reorder the terms:
-0.2222222222 + x = 0.702728369

Solving
-0.2222222222 + x = 0.702728369

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = 0.702728369 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = 0.702728369 + 0.2222222222
x = 0.702728369 + 0.2222222222

Combine like terms: 0.702728369 + 0.2222222222 = 0.9249505912
x = 0.9249505912

Simplifying
x = 0.9249505912

Subproblem 2
x + -0.2222222222 = -0.702728369

Simplifying
x + -0.2222222222 = -0.702728369

Reorder the terms:
-0.2222222222 + x = -0.702728369

Solving
-0.2222222222 + x = -0.702728369

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = -0.702728369 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = -0.702728369 + 0.2222222222
x = -0.702728369 + 0.2222222222

Combine like terms: -0.702728369 + 0.2222222222 = -0.4805061468
x = -0.4805061468

Simplifying
x = -0.4805061468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9249505912, -0.4805061468}
Solution
x = {0.9249505912, -0.4805061468}