3d(d+1)-5(d^2-2d+2)=

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Solution for 3d(d+1)-5(d^2-2d+2)= equation: 


Simplifying
3d(d + 1) + -5(d2 + -2d + 2) = 0

Reorder the terms:
3d(1 + d) + -5(d2 + -2d + 2) = 0
(1 * 3d + d * 3d) + -5(d2 + -2d + 2) = 0
(3d + 3d2) + -5(d2 + -2d + 2) = 0

Reorder the terms:
3d + 3d2 + -5(2 + -2d + d2) = 0
3d + 3d2 + (2 * -5 + -2d * -5 + d2 * -5) = 0
3d + 3d2 + (-10 + 10d + -5d2) = 0

Reorder the terms:
-10 + 3d + 10d + 3d2 + -5d2 = 0

Combine like terms: 3d + 10d = 13d
-10 + 13d + 3d2 + -5d2 = 0

Combine like terms: 3d2 + -5d2 = -2d2
-10 + 13d + -2d2 = 0

Solving
-10 + 13d + -2d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5 + -6.5d + d2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -6.5d + -5 + d2 = 0 + -5

Reorder the terms:
5 + -5 + -6.5d + d2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6.5d + d2 = 0 + -5
-6.5d + d2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6.5d + d2 = -5

The d term is -6.5d.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5d + 10.5625 + d2 = -5 + 10.5625

Reorder the terms:
10.5625 + -6.5d + d2 = -5 + 10.5625

Combine like terms: -5 + 10.5625 = 5.5625
10.5625 + -6.5d + d2 = 5.5625

Factor a perfect square on the left side:
(d + -3.25)(d + -3.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(d + -3.25) equal to 2.358495283 and -2.358495283.


Subproblem 1
d + -3.25 = 2.358495283

Simplifying
d + -3.25 = 2.358495283

Reorder the terms:
-3.25 + d = 2.358495283

Solving
-3.25 + d = 2.358495283

Solving for variable 'd'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + d = 2.358495283 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + d = 2.358495283 + 3.25
d = 2.358495283 + 3.25

Combine like terms: 2.358495283 + 3.25 = 5.608495283
d = 5.608495283

Simplifying
d = 5.608495283


Subproblem 2
d + -3.25 = -2.358495283

Simplifying
d + -3.25 = -2.358495283

Reorder the terms:
-3.25 + d = -2.358495283

Solving
-3.25 + d = -2.358495283

Solving for variable 'd'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + d = -2.358495283 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + d = -2.358495283 + 3.25
d = -2.358495283 + 3.25

Combine like terms: -2.358495283 + 3.25 = 0.891504717
d = 0.891504717

Simplifying
d = 0.891504717


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {5.608495283, 0.891504717}

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