0.2(x+60)0.4x=21

Solution for 0.2(x+60)0.4x=21 equation:

Simplifying
0.2(x + 60) * 0.4x = 21

Reorder the terms:
0.2(60 + x) * 0.4x = 21

Reorder the terms for easier multiplication:
0.2 * 0.4x(60 + x) = 21

Multiply 0.2 * 0.4
0.08x(60 + x) = 21
(60 * 0.08x + x * 0.08x) = 21
(4.8x + 0.08x2) = 21

Solving
4.8x + 0.08x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 4.8x + 0.08x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 4.8x + 0.08x2 = 0

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

Divide each side by '0.08'.
-262.5 + 60x + x2 = 0

Move the constant term to the right:

Add '262.5' to each side of the equation.
-262.5 + 60x + 262.5 + x2 = 0 + 262.5

Reorder the terms:
-262.5 + 262.5 + 60x + x2 = 0 + 262.5

Combine like terms: -262.5 + 262.5 = 0.0
0.0 + 60x + x2 = 0 + 262.5
60x + x2 = 0 + 262.5

Combine like terms: 0 + 262.5 = 262.5
60x + x2 = 262.5

The x term is 60x.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60x + 900 + x2 = 262.5 + 900

Reorder the terms:
900 + 60x + x2 = 262.5 + 900

Combine like terms: 262.5 + 900 = 1162.5
900 + 60x + x2 = 1162.5

Factor a perfect square on the left side:
(x + 30)(x + 30) = 1162.5

Calculate the square root of the right side: 34.095454242

Break this problem into two subproblems by setting 
(x + 30) equal to 34.095454242 and -34.095454242.

Subproblem 1
x + 30 = 34.095454242

Simplifying
x + 30 = 34.095454242

Reorder the terms:
30 + x = 34.095454242

Solving
30 + x = 34.095454242

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = 34.095454242 + -30

Combine like terms: 30 + -30 = 0
0 + x = 34.095454242 + -30
x = 34.095454242 + -30

Combine like terms: 34.095454242 + -30 = 4.095454242
x = 4.095454242

Simplifying
x = 4.095454242

Subproblem 2
x + 30 = -34.095454242

Simplifying
x + 30 = -34.095454242

Reorder the terms:
30 + x = -34.095454242

Solving
30 + x = -34.095454242

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = -34.095454242 + -30

Combine like terms: 30 + -30 = 0
0 + x = -34.095454242 + -30
x = -34.095454242 + -30

Combine like terms: -34.095454242 + -30 = -64.095454242
x = -64.095454242

Simplifying
x = -64.095454242

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.095454242, -64.095454242}