13x*7(-3x-1)=-63

Solution for 13x*7(-3x-1)=-63 equation:

Simplifying
13x * 7(-3x + -1) = -63

Reorder the terms:
13x * 7(-1 + -3x) = -63

Reorder the terms for easier multiplication:
13 * 7x(-1 + -3x) = -63

Multiply 13 * 7
91x(-1 + -3x) = -63
(-1 * 91x + -3x * 91x) = -63
(-91x + -273x2) = -63

Solving
-91x + -273x2 = -63

Solving for variable 'x'.

Reorder the terms:
63 + -91x + -273x2 = -63 + 63

Combine like terms: -63 + 63 = 0
63 + -91x + -273x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(9 + -13x + -39x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(9 + -13x + -39x2)' equal to zero and attempt to solve:

Simplifying
9 + -13x + -39x2 = 0

Solving
9 + -13x + -39x2 = 0

Begin completing the square.  Divide all terms by
-39 the coefficient of the squared term: 

Divide each side by '-39'.
-0.2307692308 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.2307692308' to each side of the equation.
-0.2307692308 + 0.3333333333x + 0.2307692308 + x2 = 0 + 0.2307692308

Reorder the terms:
-0.2307692308 + 0.2307692308 + 0.3333333333x + x2 = 0 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.2307692308
0.3333333333x + x2 = 0 + 0.2307692308

Combine like terms: 0 + 0.2307692308 = 0.2307692308
0.3333333333x + x2 = 0.2307692308

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.2307692308 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.2307692308 + 0.02777777779

Combine like terms: 0.2307692308 + 0.02777777779 = 0.25854700859
0.02777777779 + 0.3333333333x + x2 = 0.25854700859

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.25854700859

Calculate the square root of the right side: 0.50847518

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.50847518 and -0.50847518.

Subproblem 1
x + 0.1666666667 = 0.50847518

Simplifying
x + 0.1666666667 = 0.50847518

Reorder the terms:
0.1666666667 + x = 0.50847518

Solving
0.1666666667 + x = 0.50847518

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.50847518 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.50847518 + -0.1666666667
x = 0.50847518 + -0.1666666667

Combine like terms: 0.50847518 + -0.1666666667 = 0.3418085133
x = 0.3418085133

Simplifying
x = 0.3418085133

Subproblem 2
x + 0.1666666667 = -0.50847518

Simplifying
x + 0.1666666667 = -0.50847518

Reorder the terms:
0.1666666667 + x = -0.50847518

Solving
0.1666666667 + x = -0.50847518

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.50847518 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.50847518 + -0.1666666667
x = -0.50847518 + -0.1666666667

Combine like terms: -0.50847518 + -0.1666666667 = -0.6751418467
x = -0.6751418467

Simplifying
x = -0.6751418467

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3418085133, -0.6751418467}
Solution
x = {0.3418085133, -0.6751418467}