-5(x+4)6(x+6)=-1

Solution for -5(x+4)6(x+6)=-1 equation:

Simplifying
-5(x + 4) * 6(x + 6) = -1

Reorder the terms:
-5(4 + x) * 6(x + 6) = -1

Reorder the terms:
-5(4 + x) * 6(6 + x) = -1

Reorder the terms for easier multiplication:
-5 * 6(4 + x)(6 + x) = -1

Multiply -5 * 6
-30(4 + x)(6 + x) = -1

Multiply (4 + x) * (6 + x)
-30(4(6 + x) + x(6 + x)) = -1
-30((6 * 4 + x * 4) + x(6 + x)) = -1
-30((24 + 4x) + x(6 + x)) = -1
-30(24 + 4x + (6 * x + x * x)) = -1
-30(24 + 4x + (6x + x2)) = -1

Combine like terms: 4x + 6x = 10x
-30(24 + 10x + x2) = -1
(24 * -30 + 10x * -30 + x2 * -30) = -1
(-720 + -300x + -30x2) = -1

Solving
-720 + -300x + -30x2 = -1

Solving for variable 'x'.

Reorder the terms:
-720 + 1 + -300x + -30x2 = -1 + 1

Combine like terms: -720 + 1 = -719
-719 + -300x + -30x2 = -1 + 1

Combine like terms: -1 + 1 = 0
-719 + -300x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(719 + 300x + 30x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(719 + 300x + 30x2)' equal to zero and attempt to solve:

Simplifying
719 + 300x + 30x2 = 0

Solving
719 + 300x + 30x2 = 0

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

Divide each side by '30'.
23.96666667 + 10x + x2 = 0.0

Move the constant term to the right:

Add '-23.96666667' to each side of the equation.
23.96666667 + 10x + -23.96666667 + x2 = 0.0 + -23.96666667

Reorder the terms:
23.96666667 + -23.96666667 + 10x + x2 = 0.0 + -23.96666667

Combine like terms: 23.96666667 + -23.96666667 = 0.00000000
0.00000000 + 10x + x2 = 0.0 + -23.96666667
10x + x2 = 0.0 + -23.96666667

Combine like terms: 0.0 + -23.96666667 = -23.96666667
10x + x2 = -23.96666667

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -23.96666667 + 25

Reorder the terms:
25 + 10x + x2 = -23.96666667 + 25

Combine like terms: -23.96666667 + 25 = 1.03333333
25 + 10x + x2 = 1.03333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1.03333333

Calculate the square root of the right side: 1.016530044

Break this problem into two subproblems by setting 
(x + 5) equal to 1.016530044 and -1.016530044.

Subproblem 1
x + 5 = 1.016530044

Simplifying
x + 5 = 1.016530044

Reorder the terms:
5 + x = 1.016530044

Solving
5 + x = 1.016530044

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.016530044 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.016530044 + -5
x = 1.016530044 + -5

Combine like terms: 1.016530044 + -5 = -3.983469956
x = -3.983469956

Simplifying
x = -3.983469956

Subproblem 2
x + 5 = -1.016530044

Simplifying
x + 5 = -1.016530044

Reorder the terms:
5 + x = -1.016530044

Solving
5 + x = -1.016530044

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.016530044 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.016530044 + -5
x = -1.016530044 + -5

Combine like terms: -1.016530044 + -5 = -6.016530044
x = -6.016530044

Simplifying
x = -6.016530044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.983469956, -6.016530044}
Solution
x = {-3.983469956, -6.016530044}