7x(2x+2)=2(x+5)

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

Simplifying
7x(2x + 2) = 2(x + 5)

Reorder the terms:
7x(2 + 2x) = 2(x + 5)
(2 * 7x + 2x * 7x) = 2(x + 5)
(14x + 14x2) = 2(x + 5)

Reorder the terms:
14x + 14x2 = 2(5 + x)
14x + 14x2 = (5 * 2 + x * 2)
14x + 14x2 = (10 + 2x)

Solving
14x + 14x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + 14x + -2x + 14x2 = 10 + 2x + -10 + -2x

Combine like terms: 14x + -2x = 12x
-10 + 12x + 14x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-10 + 12x + 14x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-10 + 12x + 14x2 = 0 + 2x + -2x
-10 + 12x + 14x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + 12x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 6x + 7x2)' equal to zero and attempt to solve:

Simplifying
-5 + 6x + 7x2 = 0

Solving
-5 + 6x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.8571428571x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.8571428571x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.8571428571x + x2 = 0 + 0.7142857143
0.8571428571x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.8571428571x + x2 = 0.7142857143

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 0.7142857143 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 0.7142857143 + 0.1836734694

Combine like terms: 0.7142857143 + 0.1836734694 = 0.8979591837
0.1836734694 + 0.8571428571x + x2 = 0.8979591837

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 0.8979591837

Calculate the square root of the right side: 0.947607083

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 0.947607083 and -0.947607083.

Subproblem 1
x + 0.4285714286 = 0.947607083

Simplifying
x + 0.4285714286 = 0.947607083

Reorder the terms:
0.4285714286 + x = 0.947607083

Solving
0.4285714286 + x = 0.947607083

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = 0.947607083 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = 0.947607083 + -0.4285714286
x = 0.947607083 + -0.4285714286

Combine like terms: 0.947607083 + -0.4285714286 = 0.5190356544
x = 0.5190356544

Simplifying
x = 0.5190356544

Subproblem 2
x + 0.4285714286 = -0.947607083

Simplifying
x + 0.4285714286 = -0.947607083

Reorder the terms:
0.4285714286 + x = -0.947607083

Solving
0.4285714286 + x = -0.947607083

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = -0.947607083 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = -0.947607083 + -0.4285714286
x = -0.947607083 + -0.4285714286

Combine like terms: -0.947607083 + -0.4285714286 = -1.3761785116
x = -1.3761785116

Simplifying
x = -1.3761785116

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5190356544, -1.3761785116}
Solution
x = {0.5190356544, -1.3761785116}