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

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

Simplifying
(2x + 6)(2x + -6) = -1(2x + 9)(3x + -5)

Reorder the terms:
(6 + 2x)(2x + -6) = -1(2x + 9)(3x + -5)

Reorder the terms:
(6 + 2x)(-6 + 2x) = -1(2x + 9)(3x + -5)

Multiply (6 + 2x) * (-6 + 2x)
(6(-6 + 2x) + 2x * (-6 + 2x)) = -1(2x + 9)(3x + -5)
((-6 * 6 + 2x * 6) + 2x * (-6 + 2x)) = -1(2x + 9)(3x + -5)
((-36 + 12x) + 2x * (-6 + 2x)) = -1(2x + 9)(3x + -5)
(-36 + 12x + (-6 * 2x + 2x * 2x)) = -1(2x + 9)(3x + -5)
(-36 + 12x + (-12x + 4x2)) = -1(2x + 9)(3x + -5)

Combine like terms: 12x + -12x = 0
(-36 + 0 + 4x2) = -1(2x + 9)(3x + -5)
(-36 + 4x2) = -1(2x + 9)(3x + -5)

Reorder the terms:
-36 + 4x2 = -1(9 + 2x)(3x + -5)

Reorder the terms:
-36 + 4x2 = -1(9 + 2x)(-5 + 3x)

Multiply (9 + 2x) * (-5 + 3x)
-36 + 4x2 = -1(9(-5 + 3x) + 2x * (-5 + 3x))
-36 + 4x2 = -1((-5 * 9 + 3x * 9) + 2x * (-5 + 3x))
-36 + 4x2 = -1((-45 + 27x) + 2x * (-5 + 3x))
-36 + 4x2 = -1(-45 + 27x + (-5 * 2x + 3x * 2x))
-36 + 4x2 = -1(-45 + 27x + (-10x + 6x2))

Combine like terms: 27x + -10x = 17x
-36 + 4x2 = -1(-45 + 17x + 6x2)
-36 + 4x2 = (-45 * -1 + 17x * -1 + 6x2 * -1)
-36 + 4x2 = (45 + -17x + -6x2)

Solving
-36 + 4x2 = 45 + -17x + -6x2

Solving for variable 'x'.

Reorder the terms:
-36 + -45 + 17x + 4x2 + 6x2 = 45 + -17x + -6x2 + -45 + 17x + 6x2

Combine like terms: -36 + -45 = -81
-81 + 17x + 4x2 + 6x2 = 45 + -17x + -6x2 + -45 + 17x + 6x2

Combine like terms: 4x2 + 6x2 = 10x2
-81 + 17x + 10x2 = 45 + -17x + -6x2 + -45 + 17x + 6x2

Reorder the terms:
-81 + 17x + 10x2 = 45 + -45 + -17x + 17x + -6x2 + 6x2

Combine like terms: 45 + -45 = 0
-81 + 17x + 10x2 = 0 + -17x + 17x + -6x2 + 6x2
-81 + 17x + 10x2 = -17x + 17x + -6x2 + 6x2

Combine like terms: -17x + 17x = 0
-81 + 17x + 10x2 = 0 + -6x2 + 6x2
-81 + 17x + 10x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-81 + 17x + 10x2 = 0

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

Divide each side by '10'.
-8.1 + 1.7x + x2 = 0.0

Move the constant term to the right:

Add '8.1' to each side of the equation.
-8.1 + 1.7x + 8.1 + x2 = 0.0 + 8.1

Reorder the terms:
-8.1 + 8.1 + 1.7x + x2 = 0.0 + 8.1

Combine like terms: -8.1 + 8.1 = 0.0
0.0 + 1.7x + x2 = 0.0 + 8.1
1.7x + x2 = 0.0 + 8.1

Combine like terms: 0.0 + 8.1 = 8.1
1.7x + x2 = 8.1

The x term is 1.7x.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7x + 0.7225 + x2 = 8.1 + 0.7225

Reorder the terms:
0.7225 + 1.7x + x2 = 8.1 + 0.7225

Combine like terms: 8.1 + 0.7225 = 8.8225
0.7225 + 1.7x + x2 = 8.8225

Factor a perfect square on the left side:
(x + 0.85)(x + 0.85) = 8.8225

Calculate the square root of the right side: 2.970269348

Break this problem into two subproblems by setting 
(x + 0.85) equal to 2.970269348 and -2.970269348.

Subproblem 1
x + 0.85 = 2.970269348

Simplifying
x + 0.85 = 2.970269348

Reorder the terms:
0.85 + x = 2.970269348

Solving
0.85 + x = 2.970269348

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = 2.970269348 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = 2.970269348 + -0.85
x = 2.970269348 + -0.85

Combine like terms: 2.970269348 + -0.85 = 2.120269348
x = 2.120269348

Simplifying
x = 2.120269348

Subproblem 2
x + 0.85 = -2.970269348

Simplifying
x + 0.85 = -2.970269348

Reorder the terms:
0.85 + x = -2.970269348

Solving
0.85 + x = -2.970269348

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = -2.970269348 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = -2.970269348 + -0.85
x = -2.970269348 + -0.85

Combine like terms: -2.970269348 + -0.85 = -3.820269348
x = -3.820269348

Simplifying
x = -3.820269348

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.120269348, -3.820269348}