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

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


Simplifying
-1(5x + -5) + x(3x + -8) = 0

Reorder the terms:
-1(-5 + 5x) + x(3x + -8) = 0
(-5 * -1 + 5x * -1) + x(3x + -8) = 0
(5 + -5x) + x(3x + -8) = 0

Reorder the terms:
5 + -5x + x(-8 + 3x) = 0
5 + -5x + (-8 * x + 3x * x) = 0
5 + -5x + (-8x + 3x2) = 0

Combine like terms: -5x + -8x = -13x
5 + -13x + 3x2 = 0

Solving
5 + -13x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1.666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -4.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -4.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + -1.666666667
-4.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-4.333333333x + x2 = -1.666666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -1.666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -1.666666667 + 4.694444446

Combine like terms: -1.666666667 + 4.694444446 = 3.027777779
4.694444446 + -4.333333333x + x2 = 3.027777779

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 3.027777779

Calculate the square root of the right side: 1.740051085

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 1.740051085 and -1.740051085.


Subproblem 1
x + -2.166666667 = 1.740051085

Simplifying
x + -2.166666667 = 1.740051085

Reorder the terms:
-2.166666667 + x = 1.740051085

Solving
-2.166666667 + x = 1.740051085

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 1.740051085 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 1.740051085 + 2.166666667
x = 1.740051085 + 2.166666667

Combine like terms: 1.740051085 + 2.166666667 = 3.906717752
x = 3.906717752

Simplifying
x = 3.906717752


Subproblem 2
x + -2.166666667 = -1.740051085

Simplifying
x + -2.166666667 = -1.740051085

Reorder the terms:
-2.166666667 + x = -1.740051085

Solving
-2.166666667 + x = -1.740051085

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -1.740051085 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -1.740051085 + 2.166666667
x = -1.740051085 + 2.166666667

Combine like terms: -1.740051085 + 2.166666667 = 0.426615582
x = 0.426615582

Simplifying
x = 0.426615582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.906717752, 0.426615582}

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