2x(5x-2)-10(x-3x+6)=-8x(x+4)+4(2x-7x)

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Solution for 2x(5x-2)-10(x-3x+6)=-8x(x+4)+4(2x-7x) equation: 


Simplifying
2x(5x + -2) + -10(x + -3x + 6) = -8x(x + 4) + 4(2x + -7x)

Reorder the terms:
2x(-2 + 5x) + -10(x + -3x + 6) = -8x(x + 4) + 4(2x + -7x)
(-2 * 2x + 5x * 2x) + -10(x + -3x + 6) = -8x(x + 4) + 4(2x + -7x)
(-4x + 10x2) + -10(x + -3x + 6) = -8x(x + 4) + 4(2x + -7x)

Reorder the terms:
-4x + 10x2 + -10(6 + x + -3x) = -8x(x + 4) + 4(2x + -7x)

Combine like terms: x + -3x = -2x
-4x + 10x2 + -10(6 + -2x) = -8x(x + 4) + 4(2x + -7x)
-4x + 10x2 + (6 * -10 + -2x * -10) = -8x(x + 4) + 4(2x + -7x)
-4x + 10x2 + (-60 + 20x) = -8x(x + 4) + 4(2x + -7x)

Reorder the terms:
-60 + -4x + 20x + 10x2 = -8x(x + 4) + 4(2x + -7x)

Combine like terms: -4x + 20x = 16x
-60 + 16x + 10x2 = -8x(x + 4) + 4(2x + -7x)

Reorder the terms:
-60 + 16x + 10x2 = -8x(4 + x) + 4(2x + -7x)
-60 + 16x + 10x2 = (4 * -8x + x * -8x) + 4(2x + -7x)
-60 + 16x + 10x2 = (-32x + -8x2) + 4(2x + -7x)

Combine like terms: 2x + -7x = -5x
-60 + 16x + 10x2 = -32x + -8x2 + 4(-5x)

Remove parenthesis around (-5x)
-60 + 16x + 10x2 = -32x + -8x2 + 4 * -5x

Multiply 4 * -5
-60 + 16x + 10x2 = -32x + -8x2 + -20x

Reorder the terms:
-60 + 16x + 10x2 = -32x + -20x + -8x2

Combine like terms: -32x + -20x = -52x
-60 + 16x + 10x2 = -52x + -8x2

Solving
-60 + 16x + 10x2 = -52x + -8x2

Solving for variable 'x'.

Reorder the terms:
-60 + 16x + 52x + 10x2 + 8x2 = -52x + -8x2 + 52x + 8x2

Combine like terms: 16x + 52x = 68x
-60 + 68x + 10x2 + 8x2 = -52x + -8x2 + 52x + 8x2

Combine like terms: 10x2 + 8x2 = 18x2
-60 + 68x + 18x2 = -52x + -8x2 + 52x + 8x2

Reorder the terms:
-60 + 68x + 18x2 = -52x + 52x + -8x2 + 8x2

Combine like terms: -52x + 52x = 0
-60 + 68x + 18x2 = 0 + -8x2 + 8x2
-60 + 68x + 18x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-60 + 68x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 34x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 34x + 9x2)' equal to zero and attempt to solve:

Simplifying
-30 + 34x + 9x2 = 0

Solving
-30 + 34x + 9x2 = 0

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

Divide each side by '9'.
-3.333333333 + 3.777777778x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 3.777777778x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 3.777777778x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 3.777777778x + x2 = 0 + 3.333333333
3.777777778x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
3.777777778x + x2 = 3.333333333

The x term is 3.777777778x.  Take half its coefficient (1.888888889).
Square it (3.567901235) and add it to both sides.

Add '3.567901235' to each side of the equation.
3.777777778x + 3.567901235 + x2 = 3.333333333 + 3.567901235

Reorder the terms:
3.567901235 + 3.777777778x + x2 = 3.333333333 + 3.567901235

Combine like terms: 3.333333333 + 3.567901235 = 6.901234568
3.567901235 + 3.777777778x + x2 = 6.901234568

Factor a perfect square on the left side:
(x + 1.888888889)(x + 1.888888889) = 6.901234568

Calculate the square root of the right side: 2.627020093

Break this problem into two subproblems by setting 
(x + 1.888888889) equal to 2.627020093 and -2.627020093.


Subproblem 1
x + 1.888888889 = 2.627020093

Simplifying
x + 1.888888889 = 2.627020093

Reorder the terms:
1.888888889 + x = 2.627020093

Solving
1.888888889 + x = 2.627020093

Solving for variable 'x'.

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

Add '-1.888888889' to each side of the equation.
1.888888889 + -1.888888889 + x = 2.627020093 + -1.888888889

Combine like terms: 1.888888889 + -1.888888889 = 0.000000000
0.000000000 + x = 2.627020093 + -1.888888889
x = 2.627020093 + -1.888888889

Combine like terms: 2.627020093 + -1.888888889 = 0.738131204
x = 0.738131204

Simplifying
x = 0.738131204


Subproblem 2
x + 1.888888889 = -2.627020093

Simplifying
x + 1.888888889 = -2.627020093

Reorder the terms:
1.888888889 + x = -2.627020093

Solving
1.888888889 + x = -2.627020093

Solving for variable 'x'.

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

Add '-1.888888889' to each side of the equation.
1.888888889 + -1.888888889 + x = -2.627020093 + -1.888888889

Combine like terms: 1.888888889 + -1.888888889 = 0.000000000
0.000000000 + x = -2.627020093 + -1.888888889
x = -2.627020093 + -1.888888889

Combine like terms: -2.627020093 + -1.888888889 = -4.515908982
x = -4.515908982

Simplifying
x = -4.515908982


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.738131204, -4.515908982}
Solution
x = {0.738131204, -4.515908982}

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