0.3x(x+40)+0.1x=16

Solution for 0.3x(x+40)+0.1x=16 equation:

Simplifying
0.3x(x + 40) + 0.1x = 16

Reorder the terms:
0.3x(40 + x) + 0.1x = 16
(40 * 0.3x + x * 0.3x) + 0.1x = 16
(12x + 0.3x2) + 0.1x = 16

Reorder the terms:
12x + 0.1x + 0.3x2 = 16

Combine like terms: 12x + 0.1x = 12.1x
12.1x + 0.3x2 = 16

Solving
12.1x + 0.3x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 12.1x + 0.3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 12.1x + 0.3x2 = 0

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

Divide each side by '0.3'.
-53.33333333 + 40.33333333x + x2 = 0

Move the constant term to the right:

Add '53.33333333' to each side of the equation.
-53.33333333 + 40.33333333x + 53.33333333 + x2 = 0 + 53.33333333

Reorder the terms:
-53.33333333 + 53.33333333 + 40.33333333x + x2 = 0 + 53.33333333

Combine like terms: -53.33333333 + 53.33333333 = 0.00000000
0.00000000 + 40.33333333x + x2 = 0 + 53.33333333
40.33333333x + x2 = 0 + 53.33333333

Combine like terms: 0 + 53.33333333 = 53.33333333
40.33333333x + x2 = 53.33333333

The x term is 40.33333333x.  Take half its coefficient (20.16666667).
Square it (406.6944446) and add it to both sides.

Add '406.6944446' to each side of the equation.
40.33333333x + 406.6944446 + x2 = 53.33333333 + 406.6944446

Reorder the terms:
406.6944446 + 40.33333333x + x2 = 53.33333333 + 406.6944446

Combine like terms: 53.33333333 + 406.6944446 = 460.02777793
406.6944446 + 40.33333333x + x2 = 460.02777793

Factor a perfect square on the left side:
(x + 20.16666667)(x + 20.16666667) = 460.02777793

Calculate the square root of the right side: 21.448258156

Break this problem into two subproblems by setting 
(x + 20.16666667) equal to 21.448258156 and -21.448258156.

Subproblem 1
x + 20.16666667 = 21.448258156

Simplifying
x + 20.16666667 = 21.448258156

Reorder the terms:
20.16666667 + x = 21.448258156

Solving
20.16666667 + x = 21.448258156

Solving for variable 'x'.

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

Add '-20.16666667' to each side of the equation.
20.16666667 + -20.16666667 + x = 21.448258156 + -20.16666667

Combine like terms: 20.16666667 + -20.16666667 = 0.00000000
0.00000000 + x = 21.448258156 + -20.16666667
x = 21.448258156 + -20.16666667

Combine like terms: 21.448258156 + -20.16666667 = 1.281591486
x = 1.281591486

Simplifying
x = 1.281591486

Subproblem 2
x + 20.16666667 = -21.448258156

Simplifying
x + 20.16666667 = -21.448258156

Reorder the terms:
20.16666667 + x = -21.448258156

Solving
20.16666667 + x = -21.448258156

Solving for variable 'x'.

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

Add '-20.16666667' to each side of the equation.
20.16666667 + -20.16666667 + x = -21.448258156 + -20.16666667

Combine like terms: 20.16666667 + -20.16666667 = 0.00000000
0.00000000 + x = -21.448258156 + -20.16666667
x = -21.448258156 + -20.16666667

Combine like terms: -21.448258156 + -20.16666667 = -41.614924826
x = -41.614924826

Simplifying
x = -41.614924826

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.281591486, -41.614924826}