8-d^2=d^2+6d

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Solution for 8-d^2=d^2+6d equation: 


Simplifying
8 + -1d2 = d2 + 6d

Reorder the terms:
8 + -1d2 = 6d + d2

Solving
8 + -1d2 = 6d + d2

Solving for variable 'd'.

Reorder the terms:
8 + -6d + -1d2 + -1d2 = 6d + d2 + -6d + -1d2

Combine like terms: -1d2 + -1d2 = -2d2
8 + -6d + -2d2 = 6d + d2 + -6d + -1d2

Reorder the terms:
8 + -6d + -2d2 = 6d + -6d + d2 + -1d2

Combine like terms: 6d + -6d = 0
8 + -6d + -2d2 = 0 + d2 + -1d2
8 + -6d + -2d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
8 + -6d + -2d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -3d + -1d2) = 0

Factor a trinomial.
2((1 + -1d)(4 + d)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1d = 0

Solving
1 + -1d = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1d = 0 + -1
-1d = 0 + -1

Combine like terms: 0 + -1 = -1
-1d = -1

Divide each side by '-1'.
d = 1

Simplifying
d = 1

Subproblem 2
Set the factor '(4 + d)' equal to zero and attempt to solve:

Simplifying
4 + d = 0

Solving
4 + d = 0

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 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + d = 0 + -4
d = 0 + -4

Combine like terms: 0 + -4 = -4
d = -4

Simplifying
d = -4
Solution
d = {1, -4}

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