-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

Reorder the terms for easier multiplication:
-5.4 * 4.1x(9.6 + x) = 3.3 + -6.9x

Multiply -5.4 * 4.1
-22.14x(9.6 + x) = 3.3 + -6.9x
(9.6 * -22.14x + x * -22.14x) = 3.3 + -6.9x
(-212.544x + -22.14x2) = 3.3 + -6.9x

Solving
-212.544x + -22.14x2 = 3.3 + -6.9x

Solving for variable 'x'.

Reorder the terms:
-3.3 + -212.544x + 6.9x + -22.14x2 = 3.3 + -6.9x + -3.3 + 6.9x

Combine like terms: -212.544x + 6.9x = -205.644x
-3.3 + -205.644x + -22.14x2 = 3.3 + -6.9x + -3.3 + 6.9x

Reorder the terms:
-3.3 + -205.644x + -22.14x2 = 3.3 + -3.3 + -6.9x + 6.9x

Combine like terms: 3.3 + -3.3 = 0.0
-3.3 + -205.644x + -22.14x2 = 0.0 + -6.9x + 6.9x
-3.3 + -205.644x + -22.14x2 = -6.9x + 6.9x

Combine like terms: -6.9x + 6.9x = 0.0
-3.3 + -205.644x + -22.14x2 = 0.0

Begin completing the square.  Divide all terms by
-22.14 the coefficient of the squared term: 

Divide each side by '-22.14'.
0.1490514905 + 9.288346883x + x2 = 0

Move the constant term to the right:

Add '-0.1490514905' to each side of the equation.
0.1490514905 + 9.288346883x + -0.1490514905 + x2 = 0 + -0.1490514905

Reorder the terms:
0.1490514905 + -0.1490514905 + 9.288346883x + x2 = 0 + -0.1490514905

Combine like terms: 0.1490514905 + -0.1490514905 = 0.0000000000
0.0000000000 + 9.288346883x + x2 = 0 + -0.1490514905
9.288346883x + x2 = 0 + -0.1490514905

Combine like terms: 0 + -0.1490514905 = -0.1490514905
9.288346883x + x2 = -0.1490514905

The x term is 9.288346883x.  Take half its coefficient (4.644173442).
Square it (21.56834696) and add it to both sides.

Add '21.56834696' to each side of the equation.
9.288346883x + 21.56834696 + x2 = -0.1490514905 + 21.56834696

Reorder the terms:
21.56834696 + 9.288346883x + x2 = -0.1490514905 + 21.56834696

Combine like terms: -0.1490514905 + 21.56834696 = 21.4192954695
21.56834696 + 9.288346883x + x2 = 21.4192954695

Factor a perfect square on the left side:
(x + 4.644173442)(x + 4.644173442) = 21.4192954695

Calculate the square root of the right side: 4.628098472

Break this problem into two subproblems by setting 
(x + 4.644173442) equal to 4.628098472 and -4.628098472.

Subproblem 1
x + 4.644173442 = 4.628098472

Simplifying
x + 4.644173442 = 4.628098472

Reorder the terms:
4.644173442 + x = 4.628098472

Solving
4.644173442 + x = 4.628098472

Solving for variable 'x'.

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

Add '-4.644173442' to each side of the equation.
4.644173442 + -4.644173442 + x = 4.628098472 + -4.644173442

Combine like terms: 4.644173442 + -4.644173442 = 0.000000000
0.000000000 + x = 4.628098472 + -4.644173442
x = 4.628098472 + -4.644173442

Combine like terms: 4.628098472 + -4.644173442 = -0.01607497
x = -0.01607497

Simplifying
x = -0.01607497

Subproblem 2
x + 4.644173442 = -4.628098472

Simplifying
x + 4.644173442 = -4.628098472

Reorder the terms:
4.644173442 + x = -4.628098472

Solving
4.644173442 + x = -4.628098472

Solving for variable 'x'.

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

Add '-4.644173442' to each side of the equation.
4.644173442 + -4.644173442 + x = -4.628098472 + -4.644173442

Combine like terms: 4.644173442 + -4.644173442 = 0.000000000
0.000000000 + x = -4.628098472 + -4.644173442
x = -4.628098472 + -4.644173442

Combine like terms: -4.628098472 + -4.644173442 = -9.272271914
x = -9.272271914

Simplifying
x = -9.272271914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.01607497, -9.272271914}