6-7d(5d+6)=5

Solution for 6-7d(5d+6)=5 equation:

Simplifying
6 + -7d(5d + 6) = 5

Reorder the terms:
6 + -7d(6 + 5d) = 5
6 + (6 * -7d + 5d * -7d) = 5
6 + (-42d + -35d2) = 5

Solving
6 + -42d + -35d2 = 5

Solving for variable 'd'.

Reorder the terms:
6 + -5 + -42d + -35d2 = 5 + -5

Combine like terms: 6 + -5 = 1
1 + -42d + -35d2 = 5 + -5

Combine like terms: 5 + -5 = 0
1 + -42d + -35d2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
-0.02857142857 + 1.2d + d2 = 0

Move the constant term to the right:

Add '0.02857142857' to each side of the equation.
-0.02857142857 + 1.2d + 0.02857142857 + d2 = 0 + 0.02857142857

Reorder the terms:
-0.02857142857 + 0.02857142857 + 1.2d + d2 = 0 + 0.02857142857

Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000
0.00000000000 + 1.2d + d2 = 0 + 0.02857142857
1.2d + d2 = 0 + 0.02857142857

Combine like terms: 0 + 0.02857142857 = 0.02857142857
1.2d + d2 = 0.02857142857

The d term is 1.2d.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2d + 0.36 + d2 = 0.02857142857 + 0.36

Reorder the terms:
0.36 + 1.2d + d2 = 0.02857142857 + 0.36

Combine like terms: 0.02857142857 + 0.36 = 0.38857142857
0.36 + 1.2d + d2 = 0.38857142857

Factor a perfect square on the left side:
(d + 0.6)(d + 0.6) = 0.38857142857

Calculate the square root of the right side: 0.623354978

Break this problem into two subproblems by setting 
(d + 0.6) equal to 0.623354978 and -0.623354978.

Subproblem 1
d + 0.6 = 0.623354978

Simplifying
d + 0.6 = 0.623354978

Reorder the terms:
0.6 + d = 0.623354978

Solving
0.6 + d = 0.623354978

Solving for variable 'd'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + d = 0.623354978 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + d = 0.623354978 + -0.6
d = 0.623354978 + -0.6

Combine like terms: 0.623354978 + -0.6 = 0.023354978
d = 0.023354978

Simplifying
d = 0.023354978

Subproblem 2
d + 0.6 = -0.623354978

Simplifying
d + 0.6 = -0.623354978

Reorder the terms:
0.6 + d = -0.623354978

Solving
0.6 + d = -0.623354978

Solving for variable 'd'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + d = -0.623354978 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + d = -0.623354978 + -0.6
d = -0.623354978 + -0.6

Combine like terms: -0.623354978 + -0.6 = -1.223354978
d = -1.223354978

Simplifying
d = -1.223354978

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.023354978, -1.223354978}