5x(x+4)=10-2(x-8)

Solution for 5x(x+4)=10-2(x-8) equation:

Simplifying
5x(x + 4) = 10 + -2(x + -8)

Reorder the terms:
5x(4 + x) = 10 + -2(x + -8)
(4 * 5x + x * 5x) = 10 + -2(x + -8)
(20x + 5x2) = 10 + -2(x + -8)

Reorder the terms:
20x + 5x2 = 10 + -2(-8 + x)
20x + 5x2 = 10 + (-8 * -2 + x * -2)
20x + 5x2 = 10 + (16 + -2x)

Combine like terms: 10 + 16 = 26
20x + 5x2 = 26 + -2x

Solving
20x + 5x2 = 26 + -2x

Solving for variable 'x'.

Reorder the terms:
-26 + 20x + 2x + 5x2 = 26 + -2x + -26 + 2x

Combine like terms: 20x + 2x = 22x
-26 + 22x + 5x2 = 26 + -2x + -26 + 2x

Reorder the terms:
-26 + 22x + 5x2 = 26 + -26 + -2x + 2x

Combine like terms: 26 + -26 = 0
-26 + 22x + 5x2 = 0 + -2x + 2x
-26 + 22x + 5x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-26 + 22x + 5x2 = 0

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

Divide each side by '5'.
-5.2 + 4.4x + x2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + 4.4x + 5.2 + x2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + 4.4x + x2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + 4.4x + x2 = 0 + 5.2
4.4x + x2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
4.4x + x2 = 5.2

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 5.2 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 5.2 + 4.84

Combine like terms: 5.2 + 4.84 = 10.04
4.84 + 4.4x + x2 = 10.04

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 10.04

Calculate the square root of the right side: 3.168595904

Break this problem into two subproblems by setting 
(x + 2.2) equal to 3.168595904 and -3.168595904.

Subproblem 1
x + 2.2 = 3.168595904

Simplifying
x + 2.2 = 3.168595904

Reorder the terms:
2.2 + x = 3.168595904

Solving
2.2 + x = 3.168595904

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 3.168595904 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 3.168595904 + -2.2
x = 3.168595904 + -2.2

Combine like terms: 3.168595904 + -2.2 = 0.968595904
x = 0.968595904

Simplifying
x = 0.968595904

Subproblem 2
x + 2.2 = -3.168595904

Simplifying
x + 2.2 = -3.168595904

Reorder the terms:
2.2 + x = -3.168595904

Solving
2.2 + x = -3.168595904

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -3.168595904 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -3.168595904 + -2.2
x = -3.168595904 + -2.2

Combine like terms: -3.168595904 + -2.2 = -5.368595904
x = -5.368595904

Simplifying
x = -5.368595904

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.968595904, -5.368595904}