.2d(d-6)=.3d+5-3+.1d

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Solution for .2d(d-6)=.3d+5-3+.1d equation:


Simplifying
0.2d(d + -6) = 0.3d + 5 + -3 + 0.1d

Reorder the terms:
0.2d(-6 + d) = 0.3d + 5 + -3 + 0.1d
(-6 * 0.2d + d * 0.2d) = 0.3d + 5 + -3 + 0.1d
(-1.2d + 0.2d2) = 0.3d + 5 + -3 + 0.1d

Reorder the terms:
-1.2d + 0.2d2 = 5 + -3 + 0.3d + 0.1d

Combine like terms: 5 + -3 = 2
-1.2d + 0.2d2 = 2 + 0.3d + 0.1d

Combine like terms: 0.3d + 0.1d = 0.4d
-1.2d + 0.2d2 = 2 + 0.4d

Solving
-1.2d + 0.2d2 = 2 + 0.4d

Solving for variable 'd'.

Reorder the terms:
-2 + -1.2d + -0.4d + 0.2d2 = 2 + 0.4d + -2 + -0.4d

Combine like terms: -1.2d + -0.4d = -1.6d
-2 + -1.6d + 0.2d2 = 2 + 0.4d + -2 + -0.4d

Reorder the terms:
-2 + -1.6d + 0.2d2 = 2 + -2 + 0.4d + -0.4d

Combine like terms: 2 + -2 = 0
-2 + -1.6d + 0.2d2 = 0 + 0.4d + -0.4d
-2 + -1.6d + 0.2d2 = 0.4d + -0.4d

Combine like terms: 0.4d + -0.4d = 0.0
-2 + -1.6d + 0.2d2 = 0.0

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

Divide each side by '0.2'.
-10 + -8d + d2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -8d + 10 + d2 = 0 + 10

Reorder the terms:
-10 + 10 + -8d + d2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -8d + d2 = 0 + 10
-8d + d2 = 0 + 10

Combine like terms: 0 + 10 = 10
-8d + d2 = 10

The d term is -8d.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8d + 16 + d2 = 10 + 16

Reorder the terms:
16 + -8d + d2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8d + d2 = 26

Factor a perfect square on the left side:
(d + -4)(d + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(d + -4) equal to 5.099019514 and -5.099019514.

Subproblem 1

d + -4 = 5.099019514 Simplifying d + -4 = 5.099019514 Reorder the terms: -4 + d = 5.099019514 Solving -4 + d = 5.099019514 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + d = 5.099019514 + 4 d = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 d = 9.099019514 Simplifying d = 9.099019514

Subproblem 2

d + -4 = -5.099019514 Simplifying d + -4 = -5.099019514 Reorder the terms: -4 + d = -5.099019514 Solving -4 + d = -5.099019514 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + d = -5.099019514 + 4 d = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 d = -1.099019514 Simplifying d = -1.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. d = {9.099019514, -1.099019514}

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