(3x-9)(2x+5)=6x-8x+4

Solution for (3x-9)(2x+5)=6x-8x+4 equation:

Simplifying
(3x + -9)(2x + 5) = 6x + -8x + 4

Reorder the terms:
(-9 + 3x)(2x + 5) = 6x + -8x + 4

Reorder the terms:
(-9 + 3x)(5 + 2x) = 6x + -8x + 4

Multiply (-9 + 3x) * (5 + 2x)
(-9(5 + 2x) + 3x * (5 + 2x)) = 6x + -8x + 4
((5 * -9 + 2x * -9) + 3x * (5 + 2x)) = 6x + -8x + 4
((-45 + -18x) + 3x * (5 + 2x)) = 6x + -8x + 4
(-45 + -18x + (5 * 3x + 2x * 3x)) = 6x + -8x + 4
(-45 + -18x + (15x + 6x2)) = 6x + -8x + 4

Combine like terms: -18x + 15x = -3x
(-45 + -3x + 6x2) = 6x + -8x + 4

Reorder the terms:
-45 + -3x + 6x2 = 4 + 6x + -8x

Combine like terms: 6x + -8x = -2x
-45 + -3x + 6x2 = 4 + -2x

Solving
-45 + -3x + 6x2 = 4 + -2x

Solving for variable 'x'.

Reorder the terms:
-45 + -4 + -3x + 2x + 6x2 = 4 + -2x + -4 + 2x

Combine like terms: -45 + -4 = -49
-49 + -3x + 2x + 6x2 = 4 + -2x + -4 + 2x

Combine like terms: -3x + 2x = -1x
-49 + -1x + 6x2 = 4 + -2x + -4 + 2x

Reorder the terms:
-49 + -1x + 6x2 = 4 + -4 + -2x + 2x

Combine like terms: 4 + -4 = 0
-49 + -1x + 6x2 = 0 + -2x + 2x
-49 + -1x + 6x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-49 + -1x + 6x2 = 0

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

Divide each side by '6'.
-8.166666667 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '8.166666667' to each side of the equation.
-8.166666667 + -0.1666666667x + 8.166666667 + x2 = 0 + 8.166666667

Reorder the terms:
-8.166666667 + 8.166666667 + -0.1666666667x + x2 = 0 + 8.166666667

Combine like terms: -8.166666667 + 8.166666667 = 0.000000000
0.000000000 + -0.1666666667x + x2 = 0 + 8.166666667
-0.1666666667x + x2 = 0 + 8.166666667

Combine like terms: 0 + 8.166666667 = 8.166666667
-0.1666666667x + x2 = 8.166666667

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 8.166666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 8.166666667 + 0.006944444447

Combine like terms: 8.166666667 + 0.006944444447 = 8.173611111447
0.006944444447 + -0.1666666667x + x2 = 8.173611111447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 8.173611111447

Calculate the square root of the right side: 2.8589528

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 2.8589528 and -2.8589528.

Subproblem 1
x + -0.08333333335 = 2.8589528

Simplifying
x + -0.08333333335 = 2.8589528

Reorder the terms:
-0.08333333335 + x = 2.8589528

Solving
-0.08333333335 + x = 2.8589528

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 2.8589528 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 2.8589528 + 0.08333333335
x = 2.8589528 + 0.08333333335

Combine like terms: 2.8589528 + 0.08333333335 = 2.94228613335
x = 2.94228613335

Simplifying
x = 2.94228613335

Subproblem 2
x + -0.08333333335 = -2.8589528

Simplifying
x + -0.08333333335 = -2.8589528

Reorder the terms:
-0.08333333335 + x = -2.8589528

Solving
-0.08333333335 + x = -2.8589528

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -2.8589528 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -2.8589528 + 0.08333333335
x = -2.8589528 + 0.08333333335

Combine like terms: -2.8589528 + 0.08333333335 = -2.77561946665
x = -2.77561946665

Simplifying
x = -2.77561946665

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.94228613335, -2.77561946665}