d(3d-1)+4(d-2)=

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Solution for d(3d-1)+4(d-2)= equation: 


Simplifying
d(3d + -1) + 4(d + -2) = 0

Reorder the terms:
d(-1 + 3d) + 4(d + -2) = 0
(-1 * d + 3d * d) + 4(d + -2) = 0
(-1d + 3d2) + 4(d + -2) = 0

Reorder the terms:
-1d + 3d2 + 4(-2 + d) = 0
-1d + 3d2 + (-2 * 4 + d * 4) = 0
-1d + 3d2 + (-8 + 4d) = 0

Reorder the terms:
-8 + -1d + 4d + 3d2 = 0

Combine like terms: -1d + 4d = 3d
-8 + 3d + 3d2 = 0

Solving
-8 + 3d + 3d2 = 0

Solving for variable 'd'.

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

Divide each side by '3'.
-2.666666667 + d + d2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + d + 2.666666667 + d2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + d + d2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + d + d2 = 0 + 2.666666667
d + d2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
d + d2 = 2.666666667

The d term is d.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + d2 = 2.666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + d2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
1.25 + d2 = 2.916666667

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(d + 0.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
d + 0.5 = 1.707825128

Simplifying
d + 0.5 = 1.707825128

Reorder the terms:
0.5 + d = 1.707825128

Solving
0.5 + d = 1.707825128

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = 1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = 1.707825128 + -0.5
d = 1.707825128 + -0.5

Combine like terms: 1.707825128 + -0.5 = 1.207825128
d = 1.207825128

Simplifying
d = 1.207825128


Subproblem 2
d + 0.5 = -1.707825128

Simplifying
d + 0.5 = -1.707825128

Reorder the terms:
0.5 + d = -1.707825128

Solving
0.5 + d = -1.707825128

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = -1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = -1.707825128 + -0.5
d = -1.707825128 + -0.5

Combine like terms: -1.707825128 + -0.5 = -2.207825128
d = -2.207825128

Simplifying
d = -2.207825128


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.207825128, -2.207825128}

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