(10x+8)-3(2x+8)8(5x-2x)=

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Solution for (10x+8)-3(2x+8)8(5x-2x)= equation: 


Simplifying
(10x + 8) + -3(2x + 8) * 8(5x + -2x) = 0

Reorder the terms:
(8 + 10x) + -3(2x + 8) * 8(5x + -2x) = 0

Remove parenthesis around (8 + 10x)
8 + 10x + -3(2x + 8) * 8(5x + -2x) = 0

Reorder the terms:
8 + 10x + -3(8 + 2x) * 8(5x + -2x) = 0

Combine like terms: 5x + -2x = 3x
8 + 10x + -3(8 + 2x) * 8(3x) = 0

Remove parenthesis around (3x)
8 + 10x + -3(8 + 2x) * 8 * 3x = 0

Reorder the terms for easier multiplication:
8 + 10x + -3 * 8 * 3x(8 + 2x) = 0

Multiply -3 * 8
8 + 10x + -24 * 3x(8 + 2x) = 0

Multiply -24 * 3
8 + 10x + -72x(8 + 2x) = 0
8 + 10x + (8 * -72x + 2x * -72x) = 0
8 + 10x + (-576x + -144x2) = 0

Combine like terms: 10x + -576x = -566x
8 + -566x + -144x2 = 0

Solving
8 + -566x + -144x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -283x + -72x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -283x + -72x2)' equal to zero and attempt to solve:

Simplifying
4 + -283x + -72x2 = 0

Solving
4 + -283x + -72x2 = 0

Begin completing the square.  Divide all terms by
-72 the coefficient of the squared term: 

Divide each side by '-72'.
-0.05555555556 + 3.930555556x + x2 = 0

Move the constant term to the right:

Add '0.05555555556' to each side of the equation.
-0.05555555556 + 3.930555556x + 0.05555555556 + x2 = 0 + 0.05555555556

Reorder the terms:
-0.05555555556 + 0.05555555556 + 3.930555556x + x2 = 0 + 0.05555555556

Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000
0.00000000000 + 3.930555556x + x2 = 0 + 0.05555555556
3.930555556x + x2 = 0 + 0.05555555556

Combine like terms: 0 + 0.05555555556 = 0.05555555556
3.930555556x + x2 = 0.05555555556

The x term is 3.930555556x.  Take half its coefficient (1.965277778).
Square it (3.862316745) and add it to both sides.

Add '3.862316745' to each side of the equation.
3.930555556x + 3.862316745 + x2 = 0.05555555556 + 3.862316745

Reorder the terms:
3.862316745 + 3.930555556x + x2 = 0.05555555556 + 3.862316745

Combine like terms: 0.05555555556 + 3.862316745 = 3.91787230056
3.862316745 + 3.930555556x + x2 = 3.91787230056

Factor a perfect square on the left side:
(x + 1.965277778)(x + 1.965277778) = 3.91787230056

Calculate the square root of the right side: 1.979361589

Break this problem into two subproblems by setting 
(x + 1.965277778) equal to 1.979361589 and -1.979361589.


Subproblem 1
x + 1.965277778 = 1.979361589

Simplifying
x + 1.965277778 = 1.979361589

Reorder the terms:
1.965277778 + x = 1.979361589

Solving
1.965277778 + x = 1.979361589

Solving for variable 'x'.

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

Add '-1.965277778' to each side of the equation.
1.965277778 + -1.965277778 + x = 1.979361589 + -1.965277778

Combine like terms: 1.965277778 + -1.965277778 = 0.000000000
0.000000000 + x = 1.979361589 + -1.965277778
x = 1.979361589 + -1.965277778

Combine like terms: 1.979361589 + -1.965277778 = 0.014083811
x = 0.014083811

Simplifying
x = 0.014083811


Subproblem 2
x + 1.965277778 = -1.979361589

Simplifying
x + 1.965277778 = -1.979361589

Reorder the terms:
1.965277778 + x = -1.979361589

Solving
1.965277778 + x = -1.979361589

Solving for variable 'x'.

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

Add '-1.965277778' to each side of the equation.
1.965277778 + -1.965277778 + x = -1.979361589 + -1.965277778

Combine like terms: 1.965277778 + -1.965277778 = 0.000000000
0.000000000 + x = -1.979361589 + -1.965277778
x = -1.979361589 + -1.965277778

Combine like terms: -1.979361589 + -1.965277778 = -3.944639367
x = -3.944639367

Simplifying
x = -3.944639367


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.014083811, -3.944639367}
Solution
x = {0.014083811, -3.944639367}

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