(4-9x)(3x+2)=5

Solution for (4-9x)(3x+2)=5 equation:

Simplifying
(4 + -9x)(3x + 2) = 5

Reorder the terms:
(4 + -9x)(2 + 3x) = 5

Multiply (4 + -9x) * (2 + 3x)
(4(2 + 3x) + -9x * (2 + 3x)) = 5
((2 * 4 + 3x * 4) + -9x * (2 + 3x)) = 5
((8 + 12x) + -9x * (2 + 3x)) = 5
(8 + 12x + (2 * -9x + 3x * -9x)) = 5
(8 + 12x + (-18x + -27x2)) = 5

Combine like terms: 12x + -18x = -6x
(8 + -6x + -27x2) = 5

Solving
8 + -6x + -27x2 = 5

Solving for variable 'x'.

Reorder the terms:
8 + -5 + -6x + -27x2 = 5 + -5

Combine like terms: 8 + -5 = 3
3 + -6x + -27x2 = 5 + -5

Combine like terms: 5 + -5 = 0
3 + -6x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2x + -9x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2x + -9x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x + -9x2 = 0

Solving
1 + -2x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.1111111111 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.2222222222x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.2222222222x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.2222222222x + x2 = 0 + 0.1111111111
0.2222222222x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.2222222222x + x2 = 0.1111111111

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 0.1111111111 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 0.1111111111 + 0.01234567901

Combine like terms: 0.1111111111 + 0.01234567901 = 0.12345679011
0.01234567901 + 0.2222222222x + x2 = 0.12345679011

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 0.12345679011

Calculate the square root of the right side: 0.351364184

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 0.351364184 and -0.351364184.

Subproblem 1
x + 0.1111111111 = 0.351364184

Simplifying
x + 0.1111111111 = 0.351364184

Reorder the terms:
0.1111111111 + x = 0.351364184

Solving
0.1111111111 + x = 0.351364184

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = 0.351364184 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = 0.351364184 + -0.1111111111
x = 0.351364184 + -0.1111111111

Combine like terms: 0.351364184 + -0.1111111111 = 0.2402530729
x = 0.2402530729

Simplifying
x = 0.2402530729

Subproblem 2
x + 0.1111111111 = -0.351364184

Simplifying
x + 0.1111111111 = -0.351364184

Reorder the terms:
0.1111111111 + x = -0.351364184

Solving
0.1111111111 + x = -0.351364184

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = -0.351364184 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = -0.351364184 + -0.1111111111
x = -0.351364184 + -0.1111111111

Combine like terms: -0.351364184 + -0.1111111111 = -0.4624752951
x = -0.4624752951

Simplifying
x = -0.4624752951

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2402530729, -0.4624752951}
Solution
x = {0.2402530729, -0.4624752951}