70-(6x+14)=6x(x+5)+x

Solution for 70-(6x+14)=6x(x+5)+x equation:

Simplifying
70 + -1(6x + 14) = 6x(x + 5) + x

Reorder the terms:
70 + -1(14 + 6x) = 6x(x + 5) + x
70 + (14 * -1 + 6x * -1) = 6x(x + 5) + x
70 + (-14 + -6x) = 6x(x + 5) + x

Combine like terms: 70 + -14 = 56
56 + -6x = 6x(x + 5) + x

Reorder the terms:
56 + -6x = 6x(5 + x) + x
56 + -6x = (5 * 6x + x * 6x) + x
56 + -6x = (30x + 6x2) + x

Reorder the terms:
56 + -6x = 30x + x + 6x2

Combine like terms: 30x + x = 31x
56 + -6x = 31x + 6x2

Solving
56 + -6x = 31x + 6x2

Solving for variable 'x'.

Combine like terms: -6x + -31x = -37x
56 + -37x + -6x2 = 31x + 6x2 + -31x + -6x2

Reorder the terms:
56 + -37x + -6x2 = 31x + -31x + 6x2 + -6x2

Combine like terms: 31x + -31x = 0
56 + -37x + -6x2 = 0 + 6x2 + -6x2
56 + -37x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
56 + -37x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-9.333333333 + 6.166666667x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 6.166666667x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 6.166666667x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 6.166666667x + x2 = 0 + 9.333333333
6.166666667x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
6.166666667x + x2 = 9.333333333

The x term is 6.166666667x.  Take half its coefficient (3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
6.166666667x + 9.506944449 + x2 = 9.333333333 + 9.506944449

Reorder the terms:
9.506944449 + 6.166666667x + x2 = 9.333333333 + 9.506944449

Combine like terms: 9.333333333 + 9.506944449 = 18.840277782
9.506944449 + 6.166666667x + x2 = 18.840277782

Factor a perfect square on the left side:
(x + 3.083333334)(x + 3.083333334) = 18.840277782

Calculate the square root of the right side: 4.340538882

Break this problem into two subproblems by setting 
(x + 3.083333334) equal to 4.340538882 and -4.340538882.

Subproblem 1
x + 3.083333334 = 4.340538882

Simplifying
x + 3.083333334 = 4.340538882

Reorder the terms:
3.083333334 + x = 4.340538882

Solving
3.083333334 + x = 4.340538882

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = 4.340538882 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = 4.340538882 + -3.083333334
x = 4.340538882 + -3.083333334

Combine like terms: 4.340538882 + -3.083333334 = 1.257205548
x = 1.257205548

Simplifying
x = 1.257205548

Subproblem 2
x + 3.083333334 = -4.340538882

Simplifying
x + 3.083333334 = -4.340538882

Reorder the terms:
3.083333334 + x = -4.340538882

Solving
3.083333334 + x = -4.340538882

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = -4.340538882 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = -4.340538882 + -3.083333334
x = -4.340538882 + -3.083333334

Combine like terms: -4.340538882 + -3.083333334 = -7.423872216
x = -7.423872216

Simplifying
x = -7.423872216

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.257205548, -7.423872216}