13x(-7-10x)=2

Solution for 13x(-7-10x)=2 equation:

Simplifying
13x(-7 + -10x) = 2
(-7 * 13x + -10x * 13x) = 2
(-91x + -130x2) = 2

Solving
-91x + -130x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -91x + -130x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -91x + -130x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 91x + 130x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 91x + 130x2)' equal to zero and attempt to solve:

Simplifying
2 + 91x + 130x2 = 0

Solving
2 + 91x + 130x2 = 0

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

Divide each side by '130'.
0.01538461538 + 0.7x + x2 = 0.0

Move the constant term to the right:

Add '-0.01538461538' to each side of the equation.
0.01538461538 + 0.7x + -0.01538461538 + x2 = 0.0 + -0.01538461538

Reorder the terms:
0.01538461538 + -0.01538461538 + 0.7x + x2 = 0.0 + -0.01538461538

Combine like terms: 0.01538461538 + -0.01538461538 = 0.00000000000
0.00000000000 + 0.7x + x2 = 0.0 + -0.01538461538
0.7x + x2 = 0.0 + -0.01538461538

Combine like terms: 0.0 + -0.01538461538 = -0.01538461538
0.7x + x2 = -0.01538461538

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = -0.01538461538 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = -0.01538461538 + 0.1225

Combine like terms: -0.01538461538 + 0.1225 = 0.10711538462
0.1225 + 0.7x + x2 = 0.10711538462

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 0.10711538462

Calculate the square root of the right side: 0.327284868

Break this problem into two subproblems by setting 
(x + 0.35) equal to 0.327284868 and -0.327284868.

Subproblem 1
x + 0.35 = 0.327284868

Simplifying
x + 0.35 = 0.327284868

Reorder the terms:
0.35 + x = 0.327284868

Solving
0.35 + x = 0.327284868

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = 0.327284868 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = 0.327284868 + -0.35
x = 0.327284868 + -0.35

Combine like terms: 0.327284868 + -0.35 = -0.022715132
x = -0.022715132

Simplifying
x = -0.022715132

Subproblem 2
x + 0.35 = -0.327284868

Simplifying
x + 0.35 = -0.327284868

Reorder the terms:
0.35 + x = -0.327284868

Solving
0.35 + x = -0.327284868

Solving for variable 'x'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + x = -0.327284868 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + x = -0.327284868 + -0.35
x = -0.327284868 + -0.35

Combine like terms: -0.327284868 + -0.35 = -0.677284868
x = -0.677284868

Simplifying
x = -0.677284868

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.022715132, -0.677284868}
Solution
x = {-0.022715132, -0.677284868}