(6x+4)(2-7x)+8x(3+9x)=36

Solution for (6x+4)(2-7x)+8x(3+9x)=36 equation:

Simplifying
(6x + 4)(2 + -7x) + 8x(3 + 9x) = 36

Reorder the terms:
(4 + 6x)(2 + -7x) + 8x(3 + 9x) = 36

Multiply (4 + 6x) * (2 + -7x)
(4(2 + -7x) + 6x * (2 + -7x)) + 8x(3 + 9x) = 36
((2 * 4 + -7x * 4) + 6x * (2 + -7x)) + 8x(3 + 9x) = 36
((8 + -28x) + 6x * (2 + -7x)) + 8x(3 + 9x) = 36
(8 + -28x + (2 * 6x + -7x * 6x)) + 8x(3 + 9x) = 36
(8 + -28x + (12x + -42x2)) + 8x(3 + 9x) = 36

Combine like terms: -28x + 12x = -16x
(8 + -16x + -42x2) + 8x(3 + 9x) = 36
8 + -16x + -42x2 + (3 * 8x + 9x * 8x) = 36
8 + -16x + -42x2 + (24x + 72x2) = 36

Reorder the terms:
8 + -16x + 24x + -42x2 + 72x2 = 36

Combine like terms: -16x + 24x = 8x
8 + 8x + -42x2 + 72x2 = 36

Combine like terms: -42x2 + 72x2 = 30x2
8 + 8x + 30x2 = 36

Solving
8 + 8x + 30x2 = 36

Solving for variable 'x'.

Reorder the terms:
8 + -36 + 8x + 30x2 = 36 + -36

Combine like terms: 8 + -36 = -28
-28 + 8x + 30x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-28 + 8x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 4x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 4x + 15x2)' equal to zero and attempt to solve:

Simplifying
-14 + 4x + 15x2 = 0

Solving
-14 + 4x + 15x2 = 0

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

Divide each side by '15'.
-0.9333333333 + 0.2666666667x + x2 = 0

Move the constant term to the right:

Add '0.9333333333' to each side of the equation.
-0.9333333333 + 0.2666666667x + 0.9333333333 + x2 = 0 + 0.9333333333

Reorder the terms:
-0.9333333333 + 0.9333333333 + 0.2666666667x + x2 = 0 + 0.9333333333

Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000
0.0000000000 + 0.2666666667x + x2 = 0 + 0.9333333333
0.2666666667x + x2 = 0 + 0.9333333333

Combine like terms: 0 + 0.9333333333 = 0.9333333333
0.2666666667x + x2 = 0.9333333333

The x term is 0.2666666667x.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667x + 0.01777777780 + x2 = 0.9333333333 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667x + x2 = 0.9333333333 + 0.01777777780

Combine like terms: 0.9333333333 + 0.01777777780 = 0.9511111111
0.01777777780 + 0.2666666667x + x2 = 0.9511111111

Factor a perfect square on the left side:
(x + 0.1333333334)(x + 0.1333333334) = 0.9511111111

Calculate the square root of the right side: 0.975249256

Break this problem into two subproblems by setting 
(x + 0.1333333334) equal to 0.975249256 and -0.975249256.

Subproblem 1
x + 0.1333333334 = 0.975249256

Simplifying
x + 0.1333333334 = 0.975249256

Reorder the terms:
0.1333333334 + x = 0.975249256

Solving
0.1333333334 + x = 0.975249256

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = 0.975249256 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = 0.975249256 + -0.1333333334
x = 0.975249256 + -0.1333333334

Combine like terms: 0.975249256 + -0.1333333334 = 0.8419159226
x = 0.8419159226

Simplifying
x = 0.8419159226

Subproblem 2
x + 0.1333333334 = -0.975249256

Simplifying
x + 0.1333333334 = -0.975249256

Reorder the terms:
0.1333333334 + x = -0.975249256

Solving
0.1333333334 + x = -0.975249256

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = -0.975249256 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = -0.975249256 + -0.1333333334
x = -0.975249256 + -0.1333333334

Combine like terms: -0.975249256 + -0.1333333334 = -1.1085825894
x = -1.1085825894

Simplifying
x = -1.1085825894

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8419159226, -1.1085825894}
Solution
x = {0.8419159226, -1.1085825894}