6x=2(2x-9)(2x+1)+5

Solution for 6x=2(2x-9)(2x+1)+5 equation:

Simplifying
6x = 2(2x + -9)(2x + 1) + 5

Reorder the terms:
6x = 2(-9 + 2x)(2x + 1) + 5

Reorder the terms:
6x = 2(-9 + 2x)(1 + 2x) + 5

Multiply (-9 + 2x) * (1 + 2x)
6x = 2(-9(1 + 2x) + 2x * (1 + 2x)) + 5
6x = 2((1 * -9 + 2x * -9) + 2x * (1 + 2x)) + 5
6x = 2((-9 + -18x) + 2x * (1 + 2x)) + 5
6x = 2(-9 + -18x + (1 * 2x + 2x * 2x)) + 5
6x = 2(-9 + -18x + (2x + 4x2)) + 5

Combine like terms: -18x + 2x = -16x
6x = 2(-9 + -16x + 4x2) + 5
6x = (-9 * 2 + -16x * 2 + 4x2 * 2) + 5
6x = (-18 + -32x + 8x2) + 5

Reorder the terms:
6x = -18 + 5 + -32x + 8x2

Combine like terms: -18 + 5 = -13
6x = -13 + -32x + 8x2

Solving
6x = -13 + -32x + 8x2

Solving for variable 'x'.

Reorder the terms:
13 + 6x + 32x + -8x2 = -13 + -32x + 8x2 + 13 + 32x + -8x2

Combine like terms: 6x + 32x = 38x
13 + 38x + -8x2 = -13 + -32x + 8x2 + 13 + 32x + -8x2

Reorder the terms:
13 + 38x + -8x2 = -13 + 13 + -32x + 32x + 8x2 + -8x2

Combine like terms: -13 + 13 = 0
13 + 38x + -8x2 = 0 + -32x + 32x + 8x2 + -8x2
13 + 38x + -8x2 = -32x + 32x + 8x2 + -8x2

Combine like terms: -32x + 32x = 0
13 + 38x + -8x2 = 0 + 8x2 + -8x2
13 + 38x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
13 + 38x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.625 + -4.75x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -4.75x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -4.75x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -4.75x + x2 = 0 + 1.625
-4.75x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-4.75x + x2 = 1.625

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 1.625 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 1.625 + 5.640625

Combine like terms: 1.625 + 5.640625 = 7.265625
5.640625 + -4.75x + x2 = 7.265625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 7.265625

Calculate the square root of the right side: 2.695482332

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.695482332 and -2.695482332.

Subproblem 1
x + -2.375 = 2.695482332

Simplifying
x + -2.375 = 2.695482332

Reorder the terms:
-2.375 + x = 2.695482332

Solving
-2.375 + x = 2.695482332

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = 2.695482332 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = 2.695482332 + 2.375
x = 2.695482332 + 2.375

Combine like terms: 2.695482332 + 2.375 = 5.070482332
x = 5.070482332

Simplifying
x = 5.070482332

Subproblem 2
x + -2.375 = -2.695482332

Simplifying
x + -2.375 = -2.695482332

Reorder the terms:
-2.375 + x = -2.695482332

Solving
-2.375 + x = -2.695482332

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = -2.695482332 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = -2.695482332 + 2.375
x = -2.695482332 + 2.375

Combine like terms: -2.695482332 + 2.375 = -0.320482332
x = -0.320482332

Simplifying
x = -0.320482332

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.070482332, -0.320482332}