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

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

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

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

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

Multiply (5 + 3x) * (-9 + -2x)
(5(-9 + -2x) + 3x * (-9 + -2x)) = 4
((-9 * 5 + -2x * 5) + 3x * (-9 + -2x)) = 4
((-45 + -10x) + 3x * (-9 + -2x)) = 4
(-45 + -10x + (-9 * 3x + -2x * 3x)) = 4
(-45 + -10x + (-27x + -6x2)) = 4

Combine like terms: -10x + -27x = -37x
(-45 + -37x + -6x2) = 4

Solving
-45 + -37x + -6x2 = 4

Solving for variable 'x'.

Reorder the terms:
-45 + -4 + -37x + -6x2 = 4 + -4

Combine like terms: -45 + -4 = -49
-49 + -37x + -6x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-49 + -37x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(49 + 37x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(49 + 37x + 6x2)' equal to zero and attempt to solve:

Simplifying
49 + 37x + 6x2 = 0

Solving
49 + 37x + 6x2 = 0

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

Divide each side by '6'.
8.166666667 + 6.166666667x + x2 = 0

Move the constant term to the right:

Add '-8.166666667' to each side of the equation.
8.166666667 + 6.166666667x + -8.166666667 + x2 = 0 + -8.166666667

Reorder the terms:
8.166666667 + -8.166666667 + 6.166666667x + x2 = 0 + -8.166666667

Combine like terms: 8.166666667 + -8.166666667 = 0.000000000
0.000000000 + 6.166666667x + x2 = 0 + -8.166666667
6.166666667x + x2 = 0 + -8.166666667

Combine like terms: 0 + -8.166666667 = -8.166666667
6.166666667x + x2 = -8.166666667

The x term is 6.166666667x.  Take half its coefficient (3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
6.166666667x + 9.506944449 + x2 = -8.166666667 + 9.506944449

Reorder the terms:
9.506944449 + 6.166666667x + x2 = -8.166666667 + 9.506944449

Combine like terms: -8.166666667 + 9.506944449 = 1.340277782
9.506944449 + 6.166666667x + x2 = 1.340277782

Factor a perfect square on the left side:
(x + 3.083333334)(x + 3.083333334) = 1.340277782

Calculate the square root of the right side: 1.157703668

Break this problem into two subproblems by setting 
(x + 3.083333334) equal to 1.157703668 and -1.157703668.

Subproblem 1
x + 3.083333334 = 1.157703668

Simplifying
x + 3.083333334 = 1.157703668

Reorder the terms:
3.083333334 + x = 1.157703668

Solving
3.083333334 + x = 1.157703668

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = 1.157703668 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = 1.157703668 + -3.083333334
x = 1.157703668 + -3.083333334

Combine like terms: 1.157703668 + -3.083333334 = -1.925629666
x = -1.925629666

Simplifying
x = -1.925629666

Subproblem 2
x + 3.083333334 = -1.157703668

Simplifying
x + 3.083333334 = -1.157703668

Reorder the terms:
3.083333334 + x = -1.157703668

Solving
3.083333334 + x = -1.157703668

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = -1.157703668 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = -1.157703668 + -3.083333334
x = -1.157703668 + -3.083333334

Combine like terms: -1.157703668 + -3.083333334 = -4.241037002
x = -4.241037002

Simplifying
x = -4.241037002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.925629666, -4.241037002}
Solution
x = {-1.925629666, -4.241037002}