5x*2(x+4)=64

Solution for 5x*2(x+4)=64 equation:

Simplifying
5x * 2(x + 4) = 64

Reorder the terms:
5x * 2(4 + x) = 64

Reorder the terms for easier multiplication:
5 * 2x(4 + x) = 64

Multiply 5 * 2
10x(4 + x) = 64
(4 * 10x + x * 10x) = 64
(40x + 10x2) = 64

Solving
40x + 10x2 = 64

Solving for variable 'x'.

Reorder the terms:
-64 + 40x + 10x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 40x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 20x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-32 + 20x + 5x2)' equal to zero and attempt to solve:

Simplifying
-32 + 20x + 5x2 = 0

Solving
-32 + 20x + 5x2 = 0

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

Divide each side by '5'.
-6.4 + 4x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 4x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 4x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 4x + x2 = 0 + 6.4
4x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
4x + x2 = 6.4

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 6.4 + 4

Reorder the terms:
4 + 4x + x2 = 6.4 + 4

Combine like terms: 6.4 + 4 = 10.4
4 + 4x + x2 = 10.4

Factor a perfect square on the left side:
(x + 2)(x + 2) = 10.4

Calculate the square root of the right side: 3.224903099

Break this problem into two subproblems by setting 
(x + 2) equal to 3.224903099 and -3.224903099.

Subproblem 1
x + 2 = 3.224903099

Simplifying
x + 2 = 3.224903099

Reorder the terms:
2 + x = 3.224903099

Solving
2 + x = 3.224903099

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.224903099 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.224903099 + -2
x = 3.224903099 + -2

Combine like terms: 3.224903099 + -2 = 1.224903099
x = 1.224903099

Simplifying
x = 1.224903099

Subproblem 2
x + 2 = -3.224903099

Simplifying
x + 2 = -3.224903099

Reorder the terms:
2 + x = -3.224903099

Solving
2 + x = -3.224903099

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.224903099 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.224903099 + -2
x = -3.224903099 + -2

Combine like terms: -3.224903099 + -2 = -5.224903099
x = -5.224903099

Simplifying
x = -5.224903099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.224903099, -5.224903099}
Solution
x = {1.224903099, -5.224903099}