2x(5+7x)=4-(x-2x+3)

Solution for 2x(5+7x)=4-(x-2x+3) equation:

Simplifying
2x(5 + 7x) = 4 + -1(x + -2x + 3)
(5 * 2x + 7x * 2x) = 4 + -1(x + -2x + 3)
(10x + 14x2) = 4 + -1(x + -2x + 3)

Reorder the terms:
10x + 14x2 = 4 + -1(3 + x + -2x)

Combine like terms: x + -2x = -1x
10x + 14x2 = 4 + -1(3 + -1x)
10x + 14x2 = 4 + (3 * -1 + -1x * -1)
10x + 14x2 = 4 + (-3 + 1x)

Combine like terms: 4 + -3 = 1
10x + 14x2 = 1 + 1x

Solving
10x + 14x2 = 1 + 1x

Solving for variable 'x'.

Reorder the terms:
-1 + 10x + -1x + 14x2 = 1 + 1x + -1 + -1x

Combine like terms: 10x + -1x = 9x
-1 + 9x + 14x2 = 1 + 1x + -1 + -1x

Reorder the terms:
-1 + 9x + 14x2 = 1 + -1 + 1x + -1x

Combine like terms: 1 + -1 = 0
-1 + 9x + 14x2 = 0 + 1x + -1x
-1 + 9x + 14x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
-1 + 9x + 14x2 = 0

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

Divide each side by '14'.
-0.07142857143 + 0.6428571429x + x2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + 0.6428571429x + 0.07142857143 + x2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + 0.6428571429x + x2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + 0.6428571429x + x2 = 0 + 0.07142857143
0.6428571429x + x2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
0.6428571429x + x2 = 0.07142857143

The x term is 0.6428571429x.  Take half its coefficient (0.3214285715).
Square it (0.1033163266) and add it to both sides.

Add '0.1033163266' to each side of the equation.
0.6428571429x + 0.1033163266 + x2 = 0.07142857143 + 0.1033163266

Reorder the terms:
0.1033163266 + 0.6428571429x + x2 = 0.07142857143 + 0.1033163266

Combine like terms: 0.07142857143 + 0.1033163266 = 0.17474489803
0.1033163266 + 0.6428571429x + x2 = 0.17474489803

Factor a perfect square on the left side:
(x + 0.3214285715)(x + 0.3214285715) = 0.17474489803

Calculate the square root of the right side: 0.418024997

Break this problem into two subproblems by setting 
(x + 0.3214285715) equal to 0.418024997 and -0.418024997.

Subproblem 1
x + 0.3214285715 = 0.418024997

Simplifying
x + 0.3214285715 = 0.418024997

Reorder the terms:
0.3214285715 + x = 0.418024997

Solving
0.3214285715 + x = 0.418024997

Solving for variable 'x'.

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

Add '-0.3214285715' to each side of the equation.
0.3214285715 + -0.3214285715 + x = 0.418024997 + -0.3214285715

Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000
0.0000000000 + x = 0.418024997 + -0.3214285715
x = 0.418024997 + -0.3214285715

Combine like terms: 0.418024997 + -0.3214285715 = 0.0965964255
x = 0.0965964255

Simplifying
x = 0.0965964255

Subproblem 2
x + 0.3214285715 = -0.418024997

Simplifying
x + 0.3214285715 = -0.418024997

Reorder the terms:
0.3214285715 + x = -0.418024997

Solving
0.3214285715 + x = -0.418024997

Solving for variable 'x'.

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

Add '-0.3214285715' to each side of the equation.
0.3214285715 + -0.3214285715 + x = -0.418024997 + -0.3214285715

Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000
0.0000000000 + x = -0.418024997 + -0.3214285715
x = -0.418024997 + -0.3214285715

Combine like terms: -0.418024997 + -0.3214285715 = -0.7394535685
x = -0.7394535685

Simplifying
x = -0.7394535685

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0965964255, -0.7394535685}