(3x-6)(5x+6)=-39

Solution for (3x-6)(5x+6)=-39 equation:

Simplifying
(3x + -6)(5x + 6) = -39

Reorder the terms:
(-6 + 3x)(5x + 6) = -39

Reorder the terms:
(-6 + 3x)(6 + 5x) = -39

Multiply (-6 + 3x) * (6 + 5x)
(-6(6 + 5x) + 3x * (6 + 5x)) = -39
((6 * -6 + 5x * -6) + 3x * (6 + 5x)) = -39
((-36 + -30x) + 3x * (6 + 5x)) = -39
(-36 + -30x + (6 * 3x + 5x * 3x)) = -39
(-36 + -30x + (18x + 15x2)) = -39

Combine like terms: -30x + 18x = -12x
(-36 + -12x + 15x2) = -39

Solving
-36 + -12x + 15x2 = -39

Solving for variable 'x'.

Reorder the terms:
-36 + 39 + -12x + 15x2 = -39 + 39

Combine like terms: -36 + 39 = 3
3 + -12x + 15x2 = -39 + 39

Combine like terms: -39 + 39 = 0
3 + -12x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -4x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -4x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + -4x + 5x2 = 0

Solving
1 + -4x + 5x2 = 0

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

Divide each side by '5'.
0.2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.8x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.8x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.8x + x2 = 0 + -0.2
-0.8x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.8x + x2 = -0.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = -0.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + -0.8x + x2 = -0.04

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = -0.04

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.