(-1+-7x)(42+6x)=36

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Solution for (-1+-7x)(42+6x)=36 equation: 


Simplifying
(-1 + -7x)(42 + 6x) = 36

Multiply (-1 + -7x) * (42 + 6x)
(-1(42 + 6x) + -7x * (42 + 6x)) = 36
((42 * -1 + 6x * -1) + -7x * (42 + 6x)) = 36
((-42 + -6x) + -7x * (42 + 6x)) = 36
(-42 + -6x + (42 * -7x + 6x * -7x)) = 36
(-42 + -6x + (-294x + -42x2)) = 36

Combine like terms: -6x + -294x = -300x
(-42 + -300x + -42x2) = 36

Solving
-42 + -300x + -42x2 = 36

Solving for variable 'x'.

Reorder the terms:
-42 + -36 + -300x + -42x2 = 36 + -36

Combine like terms: -42 + -36 = -78
-78 + -300x + -42x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-78 + -300x + -42x2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(13 + 50x + 7x2) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(13 + 50x + 7x2)' equal to zero and attempt to solve:

Simplifying
13 + 50x + 7x2 = 0

Solving
13 + 50x + 7x2 = 0

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

Divide each side by '7'.
1.857142857 + 7.142857143x + x2 = 0

Move the constant term to the right:

Add '-1.857142857' to each side of the equation.
1.857142857 + 7.142857143x + -1.857142857 + x2 = 0 + -1.857142857

Reorder the terms:
1.857142857 + -1.857142857 + 7.142857143x + x2 = 0 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + 7.142857143x + x2 = 0 + -1.857142857
7.142857143x + x2 = 0 + -1.857142857

Combine like terms: 0 + -1.857142857 = -1.857142857
7.142857143x + x2 = -1.857142857

The x term is 7.142857143x.  Take half its coefficient (3.571428572).
Square it (12.75510204) and add it to both sides.

Add '12.75510204' to each side of the equation.
7.142857143x + 12.75510204 + x2 = -1.857142857 + 12.75510204

Reorder the terms:
12.75510204 + 7.142857143x + x2 = -1.857142857 + 12.75510204

Combine like terms: -1.857142857 + 12.75510204 = 10.897959183
12.75510204 + 7.142857143x + x2 = 10.897959183

Factor a perfect square on the left side:
(x + 3.571428572)(x + 3.571428572) = 10.897959183

Calculate the square root of the right side: 3.301205717

Break this problem into two subproblems by setting 
(x + 3.571428572) equal to 3.301205717 and -3.301205717.


Subproblem 1
x + 3.571428572 = 3.301205717

Simplifying
x + 3.571428572 = 3.301205717

Reorder the terms:
3.571428572 + x = 3.301205717

Solving
3.571428572 + x = 3.301205717

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = 3.301205717 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = 3.301205717 + -3.571428572
x = 3.301205717 + -3.571428572

Combine like terms: 3.301205717 + -3.571428572 = -0.270222855
x = -0.270222855

Simplifying
x = -0.270222855


Subproblem 2
x + 3.571428572 = -3.301205717

Simplifying
x + 3.571428572 = -3.301205717

Reorder the terms:
3.571428572 + x = -3.301205717

Solving
3.571428572 + x = -3.301205717

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = -3.301205717 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = -3.301205717 + -3.571428572
x = -3.301205717 + -3.571428572

Combine like terms: -3.301205717 + -3.571428572 = -6.872634289
x = -6.872634289

Simplifying
x = -6.872634289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.270222855, -6.872634289}
Solution
x = {-0.270222855, -6.872634289}

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