2x(7x+5)=13-3

Solution for 2x(7x+5)=13-3 equation:

Simplifying
2x(7x + 5) = 13 + -3

Reorder the terms:
2x(5 + 7x) = 13 + -3
(5 * 2x + 7x * 2x) = 13 + -3
(10x + 14x2) = 13 + -3

Combine like terms: 13 + -3 = 10
10x + 14x2 = 10

Solving
10x + 14x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 10x + 14x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 10x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 5x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 5x + 7x2)' equal to zero and attempt to solve:

Simplifying
-5 + 5x + 7x2 = 0

Solving
-5 + 5x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.7142857143x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.7142857143x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.7142857143x + x2 = 0 + 0.7142857143
0.7142857143x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.7142857143x + x2 = 0.7142857143

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 0.7142857143 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 0.7142857143 + 0.1275510204

Combine like terms: 0.7142857143 + 0.1275510204 = 0.8418367347
0.1275510204 + 0.7142857143x + x2 = 0.8418367347

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 0.8418367347

Calculate the square root of the right side: 0.917516613

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 0.917516613 and -0.917516613.

Subproblem 1
x + 0.3571428572 = 0.917516613

Simplifying
x + 0.3571428572 = 0.917516613

Reorder the terms:
0.3571428572 + x = 0.917516613

Solving
0.3571428572 + x = 0.917516613

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = 0.917516613 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = 0.917516613 + -0.3571428572
x = 0.917516613 + -0.3571428572

Combine like terms: 0.917516613 + -0.3571428572 = 0.5603737558
x = 0.5603737558

Simplifying
x = 0.5603737558

Subproblem 2
x + 0.3571428572 = -0.917516613

Simplifying
x + 0.3571428572 = -0.917516613

Reorder the terms:
0.3571428572 + x = -0.917516613

Solving
0.3571428572 + x = -0.917516613

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = -0.917516613 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = -0.917516613 + -0.3571428572
x = -0.917516613 + -0.3571428572

Combine like terms: -0.917516613 + -0.3571428572 = -1.2746594702
x = -1.2746594702

Simplifying
x = -1.2746594702

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5603737558, -1.2746594702}
Solution
x = {0.5603737558, -1.2746594702}