-2d(d+6)=-10

Solution for -2d(d+6)=-10 equation:

Simplifying
-2d(d + 6) = -10

Reorder the terms:
-2d(6 + d) = -10
(6 * -2d + d * -2d) = -10
(-12d + -2d2) = -10

Solving
-12d + -2d2 = -10

Solving for variable 'd'.

Reorder the terms:
10 + -12d + -2d2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -12d + -2d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6d + -1d2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -6d + -1d2)' equal to zero and attempt to solve:

Simplifying
5 + -6d + -1d2 = 0

Solving
5 + -6d + -1d2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 6d + d2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6d + 5 + d2 = 0 + 5

Reorder the terms:
-5 + 5 + 6d + d2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6d + d2 = 0 + 5
6d + d2 = 0 + 5

Combine like terms: 0 + 5 = 5
6d + d2 = 5

The d term is 6d.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6d + 9 + d2 = 5 + 9

Reorder the terms:
9 + 6d + d2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6d + d2 = 14

Factor a perfect square on the left side:
(d + 3)(d + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(d + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1
d + 3 = 3.741657387

Simplifying
d + 3 = 3.741657387

Reorder the terms:
3 + d = 3.741657387

Solving
3 + d = 3.741657387

Solving for variable 'd'.

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

Add '-3' to each side of the equation.
3 + -3 + d = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + d = 3.741657387 + -3
d = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
d = 0.741657387

Simplifying
d = 0.741657387

Subproblem 2
d + 3 = -3.741657387

Simplifying
d + 3 = -3.741657387

Reorder the terms:
3 + d = -3.741657387

Solving
3 + d = -3.741657387

Solving for variable 'd'.

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

Add '-3' to each side of the equation.
3 + -3 + d = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + d = -3.741657387 + -3
d = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
d = -6.741657387

Simplifying
d = -6.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.741657387, -6.741657387}
Solution
d = {0.741657387, -6.741657387}