x(3x-32.4)-16=0

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Solution for x(3x-32.4)-16=0 equation: 


Simplifying
x(3x + -32.4) + -16 = 0

Reorder the terms:
x(-32.4 + 3x) + -16 = 0
(-32.4 * x + 3x * x) + -16 = 0
(-32.4x + 3x2) + -16 = 0

Reorder the terms:
-16 + -32.4x + 3x2 = 0

Solving
-16 + -32.4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-5.333333333 + -10.8x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -10.8x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -10.8x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -10.8x + x2 = 0 + 5.333333333
-10.8x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-10.8x + x2 = 5.333333333

The x term is -10.8x.  Take half its coefficient (-5.4).
Square it (29.16) and add it to both sides.

Add '29.16' to each side of the equation.
-10.8x + 29.16 + x2 = 5.333333333 + 29.16

Reorder the terms:
29.16 + -10.8x + x2 = 5.333333333 + 29.16

Combine like terms: 5.333333333 + 29.16 = 34.493333333
29.16 + -10.8x + x2 = 34.493333333

Factor a perfect square on the left side:
(x + -5.4)(x + -5.4) = 34.493333333

Calculate the square root of the right side: 5.87310253

Break this problem into two subproblems by setting 
(x + -5.4) equal to 5.87310253 and -5.87310253.


Subproblem 1
x + -5.4 = 5.87310253

Simplifying
x + -5.4 = 5.87310253

Reorder the terms:
-5.4 + x = 5.87310253

Solving
-5.4 + x = 5.87310253

Solving for variable 'x'.

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

Add '5.4' to each side of the equation.
-5.4 + 5.4 + x = 5.87310253 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + x = 5.87310253 + 5.4
x = 5.87310253 + 5.4

Combine like terms: 5.87310253 + 5.4 = 11.27310253
x = 11.27310253

Simplifying
x = 11.27310253


Subproblem 2
x + -5.4 = -5.87310253

Simplifying
x + -5.4 = -5.87310253

Reorder the terms:
-5.4 + x = -5.87310253

Solving
-5.4 + x = -5.87310253

Solving for variable 'x'.

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

Add '5.4' to each side of the equation.
-5.4 + 5.4 + x = -5.87310253 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + x = -5.87310253 + 5.4
x = -5.87310253 + 5.4

Combine like terms: -5.87310253 + 5.4 = -0.47310253
x = -0.47310253

Simplifying
x = -0.47310253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.27310253, -0.47310253}

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