-4x(2x+9)+3x=6-4(x-3)

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

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

Reorder the terms:
-4x(9 + 2x) + 3x = 6 + -4(x + -3)
(9 * -4x + 2x * -4x) + 3x = 6 + -4(x + -3)
(-36x + -8x2) + 3x = 6 + -4(x + -3)

Reorder the terms:
-36x + 3x + -8x2 = 6 + -4(x + -3)

Combine like terms: -36x + 3x = -33x
-33x + -8x2 = 6 + -4(x + -3)

Reorder the terms:
-33x + -8x2 = 6 + -4(-3 + x)
-33x + -8x2 = 6 + (-3 * -4 + x * -4)
-33x + -8x2 = 6 + (12 + -4x)

Combine like terms: 6 + 12 = 18
-33x + -8x2 = 18 + -4x

Solving
-33x + -8x2 = 18 + -4x

Solving for variable 'x'.

Reorder the terms:
-18 + -33x + 4x + -8x2 = 18 + -4x + -18 + 4x

Combine like terms: -33x + 4x = -29x
-18 + -29x + -8x2 = 18 + -4x + -18 + 4x

Reorder the terms:
-18 + -29x + -8x2 = 18 + -18 + -4x + 4x

Combine like terms: 18 + -18 = 0
-18 + -29x + -8x2 = 0 + -4x + 4x
-18 + -29x + -8x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-18 + -29x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 29x + 8x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(18 + 29x + 8x2)' equal to zero and attempt to solve:

Simplifying
18 + 29x + 8x2 = 0

Solving
18 + 29x + 8x2 = 0

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

Divide each side by '8'.
2.25 + 3.625x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 3.625x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 3.625x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 3.625x + x2 = 0 + -2.25
3.625x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
3.625x + x2 = -2.25

The x term is 3.625x.  Take half its coefficient (1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
3.625x + 3.28515625 + x2 = -2.25 + 3.28515625

Reorder the terms:
3.28515625 + 3.625x + x2 = -2.25 + 3.28515625

Combine like terms: -2.25 + 3.28515625 = 1.03515625
3.28515625 + 3.625x + x2 = 1.03515625

Factor a perfect square on the left side:
(x + 1.8125)(x + 1.8125) = 1.03515625

Calculate the square root of the right side: 1.017426287

Break this problem into two subproblems by setting 
(x + 1.8125) equal to 1.017426287 and -1.017426287.

Subproblem 1
x + 1.8125 = 1.017426287

Simplifying
x + 1.8125 = 1.017426287

Reorder the terms:
1.8125 + x = 1.017426287

Solving
1.8125 + x = 1.017426287

Solving for variable 'x'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + x = 1.017426287 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + x = 1.017426287 + -1.8125
x = 1.017426287 + -1.8125

Combine like terms: 1.017426287 + -1.8125 = -0.795073713
x = -0.795073713

Simplifying
x = -0.795073713

Subproblem 2
x + 1.8125 = -1.017426287

Simplifying
x + 1.8125 = -1.017426287

Reorder the terms:
1.8125 + x = -1.017426287

Solving
1.8125 + x = -1.017426287

Solving for variable 'x'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + x = -1.017426287 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + x = -1.017426287 + -1.8125
x = -1.017426287 + -1.8125

Combine like terms: -1.017426287 + -1.8125 = -2.829926287
x = -2.829926287

Simplifying
x = -2.829926287

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.795073713, -2.829926287}
Solution
x = {-0.795073713, -2.829926287}