-3(2d)=d^2-3

Solution for -3(2d)=d^2-3 equation:

Simplifying
-3(2d) = d2 + -3

Remove parenthesis around (2d)
-3 * 2d = d2 + -3

Multiply -3 * 2
-6d = d2 + -3

Reorder the terms:
-6d = -3 + d2

Solving
-6d = -3 + d2

Solving for variable 'd'.

Reorder the terms:
3 + -6d + -1d2 = -3 + d2 + 3 + -1d2

Reorder the terms:
3 + -6d + -1d2 = -3 + 3 + d2 + -1d2

Combine like terms: -3 + 3 = 0
3 + -6d + -1d2 = 0 + d2 + -1d2
3 + -6d + -1d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
3 + -6d + -1d2 = 0

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

Divide each side by '-1'.
-3 + 6d + d2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6d + 3 + d2 = 0 + 3

Reorder the terms:
-3 + 3 + 6d + d2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6d + d2 = 0 + 3
6d + d2 = 0 + 3

Combine like terms: 0 + 3 = 3
6d + d2 = 3

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 = 3 + 9

Reorder the terms:
9 + 6d + d2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6d + d2 = 12

Factor a perfect square on the left side:
(d + 3)(d + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(d + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
d + 3 = 3.464101615

Simplifying
d + 3 = 3.464101615

Reorder the terms:
3 + d = 3.464101615

Solving
3 + d = 3.464101615

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 = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + d = 3.464101615 + -3
d = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
d = 0.464101615

Simplifying
d = 0.464101615

Subproblem 2
d + 3 = -3.464101615

Simplifying
d + 3 = -3.464101615

Reorder the terms:
3 + d = -3.464101615

Solving
3 + d = -3.464101615

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 = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + d = -3.464101615 + -3
d = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
d = -6.464101615

Simplifying
d = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.464101615, -6.464101615}