2(3+5)=5(2x-4)4x

Solution for 2(3+5)=5(2x-4)4x equation:

Simplifying
2(3 + 5) = 5(2x + -4) * 4x

Combine like terms: 3 + 5 = 8
2(8) = 5(2x + -4) * 4x

Multiply 2 * 8
16 = 5(2x + -4) * 4x

Reorder the terms:
16 = 5(-4 + 2x) * 4x

Reorder the terms for easier multiplication:
16 = 5 * 4x(-4 + 2x)

Multiply 5 * 4
16 = 20x(-4 + 2x)
16 = (-4 * 20x + 2x * 20x)
16 = (-80x + 40x2)

Solving
16 = -80x + 40x2

Solving for variable 'x'.

Reorder the terms:
16 + 80x + -40x2 = -80x + 80x + 40x2 + -40x2

Combine like terms: -80x + 80x = 0
16 + 80x + -40x2 = 0 + 40x2 + -40x2
16 + 80x + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
16 + 80x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + 10x + -5x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(2 + 10x + -5x2)' equal to zero and attempt to solve:

Simplifying
2 + 10x + -5x2 = 0

Solving
2 + 10x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + -2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -2x + x2 = 0 + 0.4
-2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-2x + x2 = 0.4

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 = 0.4 + 1

Reorder the terms:
1 + -2x + x2 = 0.4 + 1

Combine like terms: 0.4 + 1 = 1.4
1 + -2x + x2 = 1.4

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(x + -1) equal to 1.183215957 and -1.183215957.

Subproblem 1
x + -1 = 1.183215957

Simplifying
x + -1 = 1.183215957

Reorder the terms:
-1 + x = 1.183215957

Solving
-1 + x = 1.183215957

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 = 1.183215957 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.183215957 + 1
x = 1.183215957 + 1

Combine like terms: 1.183215957 + 1 = 2.183215957
x = 2.183215957

Simplifying
x = 2.183215957

Subproblem 2
x + -1 = -1.183215957

Simplifying
x + -1 = -1.183215957

Reorder the terms:
-1 + x = -1.183215957

Solving
-1 + x = -1.183215957

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 = -1.183215957 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.183215957 + 1
x = -1.183215957 + 1

Combine like terms: -1.183215957 + 1 = -0.183215957
x = -0.183215957

Simplifying
x = -0.183215957

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.183215957, -0.183215957}
Solution
x = {2.183215957, -0.183215957}