240=4(2x+4)x

Solution for 240=4(2x+4)x equation:

Simplifying
240 = 4(2x + 4) * x

Reorder the terms:
240 = 4(4 + 2x) * x

Reorder the terms for easier multiplication:
240 = 4x(4 + 2x)
240 = (4 * 4x + 2x * 4x)
240 = (16x + 8x2)

Solving
240 = 16x + 8x2

Solving for variable 'x'.

Reorder the terms:
240 + -16x + -8x2 = 16x + -16x + 8x2 + -8x2

Combine like terms: 16x + -16x = 0
240 + -16x + -8x2 = 0 + 8x2 + -8x2
240 + -16x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
240 + -16x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(30 + -2x + -1x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(30 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
30 + -2x + -1x2 = 0

Solving
30 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + 2x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2x + x2 = 0 + 30
2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
2x + x2 = 30

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 30 + 1

Reorder the terms:
1 + 2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2x + x2 = 31

Factor a perfect square on the left side:
(x + 1)(x + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + 1 = 5.567764363

Simplifying
x + 1 = 5.567764363

Reorder the terms:
1 + x = 5.567764363

Solving
1 + x = 5.567764363

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.567764363 + -1
x = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
x = 4.567764363

Simplifying
x = 4.567764363

Subproblem 2
x + 1 = -5.567764363

Simplifying
x + 1 = -5.567764363

Reorder the terms:
1 + x = -5.567764363

Solving
1 + x = -5.567764363

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.567764363 + -1
x = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
x = -6.567764363

Simplifying
x = -6.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.567764363, -6.567764363}
Solution
x = {4.567764363, -6.567764363}