3(4d+1)9d=6(2-d)

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Solution for 3(4d+1)9d=6(2-d) equation:


Simplifying
3(4d + 1) * 9d = 6(2 + -1d)

Reorder the terms:
3(1 + 4d) * 9d = 6(2 + -1d)

Reorder the terms for easier multiplication:
3 * 9d(1 + 4d) = 6(2 + -1d)

Multiply 3 * 9
27d(1 + 4d) = 6(2 + -1d)
(1 * 27d + 4d * 27d) = 6(2 + -1d)
(27d + 108d2) = 6(2 + -1d)
27d + 108d2 = (2 * 6 + -1d * 6)
27d + 108d2 = (12 + -6d)

Solving
27d + 108d2 = 12 + -6d

Solving for variable 'd'.

Reorder the terms:
-12 + 27d + 6d + 108d2 = 12 + -6d + -12 + 6d

Combine like terms: 27d + 6d = 33d
-12 + 33d + 108d2 = 12 + -6d + -12 + 6d

Reorder the terms:
-12 + 33d + 108d2 = 12 + -12 + -6d + 6d

Combine like terms: 12 + -12 = 0
-12 + 33d + 108d2 = 0 + -6d + 6d
-12 + 33d + 108d2 = -6d + 6d

Combine like terms: -6d + 6d = 0
-12 + 33d + 108d2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 11d + 36d2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 11d + 36d2)' equal to zero and attempt to solve:

Simplifying
-4 + 11d + 36d2 = 0

Solving
-4 + 11d + 36d2 = 0

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

Divide each side by '36'.
-0.1111111111 + 0.3055555556d + d2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.3055555556d + 0.1111111111 + d2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.3055555556d + d2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.3055555556d + d2 = 0 + 0.1111111111
0.3055555556d + d2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.3055555556d + d2 = 0.1111111111

The d term is 0.3055555556d.  Take half its coefficient (0.1527777778).
Square it (0.02334104939) and add it to both sides.

Add '0.02334104939' to each side of the equation.
0.3055555556d + 0.02334104939 + d2 = 0.1111111111 + 0.02334104939

Reorder the terms:
0.02334104939 + 0.3055555556d + d2 = 0.1111111111 + 0.02334104939

Combine like terms: 0.1111111111 + 0.02334104939 = 0.13445216049
0.02334104939 + 0.3055555556d + d2 = 0.13445216049

Factor a perfect square on the left side:
(d + 0.1527777778)(d + 0.1527777778) = 0.13445216049

Calculate the square root of the right side: 0.366677188

Break this problem into two subproblems by setting 
(d + 0.1527777778) equal to 0.366677188 and -0.366677188.


Subproblem 1
d + 0.1527777778 = 0.366677188

Simplifying
d + 0.1527777778 = 0.366677188

Reorder the terms:
0.1527777778 + d = 0.366677188

Solving
0.1527777778 + d = 0.366677188

Solving for variable 'd'.

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

Add '-0.1527777778' to each side of the equation.
0.1527777778 + -0.1527777778 + d = 0.366677188 + -0.1527777778

Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000
0.0000000000 + d = 0.366677188 + -0.1527777778
d = 0.366677188 + -0.1527777778

Combine like terms: 0.366677188 + -0.1527777778 = 0.2138994102
d = 0.2138994102

Simplifying
d = 0.2138994102


Subproblem 2
d + 0.1527777778 = -0.366677188

Simplifying
d + 0.1527777778 = -0.366677188

Reorder the terms:
0.1527777778 + d = -0.366677188

Solving
0.1527777778 + d = -0.366677188

Solving for variable 'd'.

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

Add '-0.1527777778' to each side of the equation.
0.1527777778 + -0.1527777778 + d = -0.366677188 + -0.1527777778

Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000
0.0000000000 + d = -0.366677188 + -0.1527777778
d = -0.366677188 + -0.1527777778

Combine like terms: -0.366677188 + -0.1527777778 = -0.5194549658
d = -0.5194549658

Simplifying
d = -0.5194549658


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.2138994102, -0.5194549658}
Solution
d = {0.2138994102, -0.5194549658}

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