-5.4x(x+9.6)+4.1=3.3-6.9x

Solution for -5.4x(x+9.6)+4.1=3.3-6.9x equation:

Simplifying
-5.4x(x + 9.6) + 4.1 = 3.3 + -6.9x

Reorder the terms:
-5.4x(9.6 + x) + 4.1 = 3.3 + -6.9x
(9.6 * -5.4x + x * -5.4x) + 4.1 = 3.3 + -6.9x
(-51.84x + -5.4x2) + 4.1 = 3.3 + -6.9x

Reorder the terms:
4.1 + -51.84x + -5.4x2 = 3.3 + -6.9x

Solving
4.1 + -51.84x + -5.4x2 = 3.3 + -6.9x

Solving for variable 'x'.

Reorder the terms:
4.1 + -3.3 + -51.84x + 6.9x + -5.4x2 = 3.3 + -6.9x + -3.3 + 6.9x

Combine like terms: 4.1 + -3.3 = 0.8
0.8 + -51.84x + 6.9x + -5.4x2 = 3.3 + -6.9x + -3.3 + 6.9x

Combine like terms: -51.84x + 6.9x = -44.94x
0.8 + -44.94x + -5.4x2 = 3.3 + -6.9x + -3.3 + 6.9x

Reorder the terms:
0.8 + -44.94x + -5.4x2 = 3.3 + -3.3 + -6.9x + 6.9x

Combine like terms: 3.3 + -3.3 = 0.0
0.8 + -44.94x + -5.4x2 = 0.0 + -6.9x + 6.9x
0.8 + -44.94x + -5.4x2 = -6.9x + 6.9x

Combine like terms: -6.9x + 6.9x = 0.0
0.8 + -44.94x + -5.4x2 = 0.0

Begin completing the square.  Divide all terms by
-5.4 the coefficient of the squared term: 

Divide each side by '-5.4'.
-0.1481481481 + 8.322222222x + x2 = 0

Move the constant term to the right:

Add '0.1481481481' to each side of the equation.
-0.1481481481 + 8.322222222x + 0.1481481481 + x2 = 0 + 0.1481481481

Reorder the terms:
-0.1481481481 + 0.1481481481 + 8.322222222x + x2 = 0 + 0.1481481481

Combine like terms: -0.1481481481 + 0.1481481481 = 0.0000000000
0.0000000000 + 8.322222222x + x2 = 0 + 0.1481481481
8.322222222x + x2 = 0 + 0.1481481481

Combine like terms: 0 + 0.1481481481 = 0.1481481481
8.322222222x + x2 = 0.1481481481

The x term is 8.322222222x.  Take half its coefficient (4.161111111).
Square it (17.31484568) and add it to both sides.

Add '17.31484568' to each side of the equation.
8.322222222x + 17.31484568 + x2 = 0.1481481481 + 17.31484568

Reorder the terms:
17.31484568 + 8.322222222x + x2 = 0.1481481481 + 17.31484568

Combine like terms: 0.1481481481 + 17.31484568 = 17.4629938281
17.31484568 + 8.322222222x + x2 = 17.4629938281

Factor a perfect square on the left side:
(x + 4.161111111)(x + 4.161111111) = 17.4629938281

Calculate the square root of the right side: 4.178874708

Break this problem into two subproblems by setting 
(x + 4.161111111) equal to 4.178874708 and -4.178874708.

Subproblem 1
x + 4.161111111 = 4.178874708

Simplifying
x + 4.161111111 = 4.178874708

Reorder the terms:
4.161111111 + x = 4.178874708

Solving
4.161111111 + x = 4.178874708

Solving for variable 'x'.

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

Add '-4.161111111' to each side of the equation.
4.161111111 + -4.161111111 + x = 4.178874708 + -4.161111111

Combine like terms: 4.161111111 + -4.161111111 = 0.000000000
0.000000000 + x = 4.178874708 + -4.161111111
x = 4.178874708 + -4.161111111

Combine like terms: 4.178874708 + -4.161111111 = 0.017763597
x = 0.017763597

Simplifying
x = 0.017763597

Subproblem 2
x + 4.161111111 = -4.178874708

Simplifying
x + 4.161111111 = -4.178874708

Reorder the terms:
4.161111111 + x = -4.178874708

Solving
4.161111111 + x = -4.178874708

Solving for variable 'x'.

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

Add '-4.161111111' to each side of the equation.
4.161111111 + -4.161111111 + x = -4.178874708 + -4.161111111

Combine like terms: 4.161111111 + -4.161111111 = 0.000000000
0.000000000 + x = -4.178874708 + -4.161111111
x = -4.178874708 + -4.161111111

Combine like terms: -4.178874708 + -4.161111111 = -8.339985819
x = -8.339985819

Simplifying
x = -8.339985819

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.017763597, -8.339985819}