38x+36=5(x+2)*7x+4

Solution for 38x+36=5(x+2)*7x+4 equation:

Simplifying
38x + 36 = 5(x + 2) * 7x + 4

Reorder the terms:
36 + 38x = 5(x + 2) * 7x + 4

Reorder the terms:
36 + 38x = 5(2 + x) * 7x + 4

Reorder the terms for easier multiplication:
36 + 38x = 5 * 7x(2 + x) + 4

Multiply 5 * 7
36 + 38x = 35x(2 + x) + 4
36 + 38x = (2 * 35x + x * 35x) + 4
36 + 38x = (70x + 35x2) + 4

Reorder the terms:
36 + 38x = 4 + 70x + 35x2

Solving
36 + 38x = 4 + 70x + 35x2

Solving for variable 'x'.

Reorder the terms:
36 + -4 + 38x + -70x + -35x2 = 4 + 70x + 35x2 + -4 + -70x + -35x2

Combine like terms: 36 + -4 = 32
32 + 38x + -70x + -35x2 = 4 + 70x + 35x2 + -4 + -70x + -35x2

Combine like terms: 38x + -70x = -32x
32 + -32x + -35x2 = 4 + 70x + 35x2 + -4 + -70x + -35x2

Reorder the terms:
32 + -32x + -35x2 = 4 + -4 + 70x + -70x + 35x2 + -35x2

Combine like terms: 4 + -4 = 0
32 + -32x + -35x2 = 0 + 70x + -70x + 35x2 + -35x2
32 + -32x + -35x2 = 70x + -70x + 35x2 + -35x2

Combine like terms: 70x + -70x = 0
32 + -32x + -35x2 = 0 + 35x2 + -35x2
32 + -32x + -35x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
32 + -32x + -35x2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
-0.9142857143 + 0.9142857143x + x2 = 0

Move the constant term to the right:

Add '0.9142857143' to each side of the equation.
-0.9142857143 + 0.9142857143x + 0.9142857143 + x2 = 0 + 0.9142857143

Reorder the terms:
-0.9142857143 + 0.9142857143 + 0.9142857143x + x2 = 0 + 0.9142857143

Combine like terms: -0.9142857143 + 0.9142857143 = 0.0000000000
0.0000000000 + 0.9142857143x + x2 = 0 + 0.9142857143
0.9142857143x + x2 = 0 + 0.9142857143

Combine like terms: 0 + 0.9142857143 = 0.9142857143
0.9142857143x + x2 = 0.9142857143

The x term is 0.9142857143x.  Take half its coefficient (0.4571428572).
Square it (0.2089795919) and add it to both sides.

Add '0.2089795919' to each side of the equation.
0.9142857143x + 0.2089795919 + x2 = 0.9142857143 + 0.2089795919

Reorder the terms:
0.2089795919 + 0.9142857143x + x2 = 0.9142857143 + 0.2089795919

Combine like terms: 0.9142857143 + 0.2089795919 = 1.1232653062
0.2089795919 + 0.9142857143x + x2 = 1.1232653062

Factor a perfect square on the left side:
(x + 0.4571428572)(x + 0.4571428572) = 1.1232653062

Calculate the square root of the right side: 1.059842114

Break this problem into two subproblems by setting 
(x + 0.4571428572) equal to 1.059842114 and -1.059842114.

Subproblem 1
x + 0.4571428572 = 1.059842114

Simplifying
x + 0.4571428572 = 1.059842114

Reorder the terms:
0.4571428572 + x = 1.059842114

Solving
0.4571428572 + x = 1.059842114

Solving for variable 'x'.

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

Add '-0.4571428572' to each side of the equation.
0.4571428572 + -0.4571428572 + x = 1.059842114 + -0.4571428572

Combine like terms: 0.4571428572 + -0.4571428572 = 0.0000000000
0.0000000000 + x = 1.059842114 + -0.4571428572
x = 1.059842114 + -0.4571428572

Combine like terms: 1.059842114 + -0.4571428572 = 0.6026992568
x = 0.6026992568

Simplifying
x = 0.6026992568

Subproblem 2
x + 0.4571428572 = -1.059842114

Simplifying
x + 0.4571428572 = -1.059842114

Reorder the terms:
0.4571428572 + x = -1.059842114

Solving
0.4571428572 + x = -1.059842114

Solving for variable 'x'.

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

Add '-0.4571428572' to each side of the equation.
0.4571428572 + -0.4571428572 + x = -1.059842114 + -0.4571428572

Combine like terms: 0.4571428572 + -0.4571428572 = 0.0000000000
0.0000000000 + x = -1.059842114 + -0.4571428572
x = -1.059842114 + -0.4571428572

Combine like terms: -1.059842114 + -0.4571428572 = -1.5169849712
x = -1.5169849712

Simplifying
x = -1.5169849712

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6026992568, -1.5169849712}