2x+4x*(28-x)=80

Solution for 2x+4x*(28-x)=80 equation:

Simplifying
2x + 4x(28 + -1x) = 80
2x + (28 * 4x + -1x * 4x) = 80
2x + (112x + -4x2) = 80

Combine like terms: 2x + 112x = 114x
114x + -4x2 = 80

Solving
114x + -4x2 = 80

Solving for variable 'x'.

Reorder the terms:
-80 + 114x + -4x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 114x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 57x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-40 + 57x + -2x2)' equal to zero and attempt to solve:

Simplifying
-40 + 57x + -2x2 = 0

Solving
-40 + 57x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
20 + -28.5x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -28.5x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -28.5x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -28.5x + x2 = 0 + -20
-28.5x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-28.5x + x2 = -20

The x term is -28.5x.  Take half its coefficient (-14.25).
Square it (203.0625) and add it to both sides.

Add '203.0625' to each side of the equation.
-28.5x + 203.0625 + x2 = -20 + 203.0625

Reorder the terms:
203.0625 + -28.5x + x2 = -20 + 203.0625

Combine like terms: -20 + 203.0625 = 183.0625
203.0625 + -28.5x + x2 = 183.0625

Factor a perfect square on the left side:
(x + -14.25)(x + -14.25) = 183.0625

Calculate the square root of the right side: 13.530059128

Break this problem into two subproblems by setting 
(x + -14.25) equal to 13.530059128 and -13.530059128.

Subproblem 1
x + -14.25 = 13.530059128

Simplifying
x + -14.25 = 13.530059128

Reorder the terms:
-14.25 + x = 13.530059128

Solving
-14.25 + x = 13.530059128

Solving for variable 'x'.

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

Add '14.25' to each side of the equation.
-14.25 + 14.25 + x = 13.530059128 + 14.25

Combine like terms: -14.25 + 14.25 = 0.00
0.00 + x = 13.530059128 + 14.25
x = 13.530059128 + 14.25

Combine like terms: 13.530059128 + 14.25 = 27.780059128
x = 27.780059128

Simplifying
x = 27.780059128

Subproblem 2
x + -14.25 = -13.530059128

Simplifying
x + -14.25 = -13.530059128

Reorder the terms:
-14.25 + x = -13.530059128

Solving
-14.25 + x = -13.530059128

Solving for variable 'x'.

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

Add '14.25' to each side of the equation.
-14.25 + 14.25 + x = -13.530059128 + 14.25

Combine like terms: -14.25 + 14.25 = 0.00
0.00 + x = -13.530059128 + 14.25
x = -13.530059128 + 14.25

Combine like terms: -13.530059128 + 14.25 = 0.719940872
x = 0.719940872

Simplifying
x = 0.719940872

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.780059128, 0.719940872}
Solution
x = {27.780059128, 0.719940872}