2(2x-5)+2x(3x-10)=70

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Solution for 2(2x-5)+2x(3x-10)=70 equation: 


Simplifying
2(2x + -5) + 2x(3x + -10) = 70

Reorder the terms:
2(-5 + 2x) + 2x(3x + -10) = 70
(-5 * 2 + 2x * 2) + 2x(3x + -10) = 70
(-10 + 4x) + 2x(3x + -10) = 70

Reorder the terms:
-10 + 4x + 2x(-10 + 3x) = 70
-10 + 4x + (-10 * 2x + 3x * 2x) = 70
-10 + 4x + (-20x + 6x2) = 70

Combine like terms: 4x + -20x = -16x
-10 + -16x + 6x2 = 70

Solving
-10 + -16x + 6x2 = 70

Solving for variable 'x'.

Reorder the terms:
-10 + -70 + -16x + 6x2 = 70 + -70

Combine like terms: -10 + -70 = -80
-80 + -16x + 6x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-80 + -16x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
-40 + -8x + 3x2 = 0

Solving
-40 + -8x + 3x2 = 0

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

Divide each side by '3'.
-13.33333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -2.666666667x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -2.666666667x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 13.33333333
-2.666666667x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-2.666666667x + x2 = 13.33333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 13.33333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 13.33333333 + 1.777777780

Combine like terms: 13.33333333 + 1.777777780 = 15.11111111
1.777777780 + -2.666666667x + x2 = 15.11111111

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 15.11111111

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 3.887301263 and -3.887301263.


Subproblem 1
x + -1.333333334 = 3.887301263

Simplifying
x + -1.333333334 = 3.887301263

Reorder the terms:
-1.333333334 + x = 3.887301263

Solving
-1.333333334 + x = 3.887301263

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 3.887301263 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 3.887301263 + 1.333333334
x = 3.887301263 + 1.333333334

Combine like terms: 3.887301263 + 1.333333334 = 5.220634597
x = 5.220634597

Simplifying
x = 5.220634597


Subproblem 2
x + -1.333333334 = -3.887301263

Simplifying
x + -1.333333334 = -3.887301263

Reorder the terms:
-1.333333334 + x = -3.887301263

Solving
-1.333333334 + x = -3.887301263

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -3.887301263 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -3.887301263 + 1.333333334
x = -3.887301263 + 1.333333334

Combine like terms: -3.887301263 + 1.333333334 = -2.553967929
x = -2.553967929

Simplifying
x = -2.553967929


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.220634597, -2.553967929}
Solution
x = {5.220634597, -2.553967929}

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