(7D+9)(D+7)=47

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Solution for (7D+9)(D+7)=47 equation: 


Simplifying
(7D + 9)(D + 7) = 47

Reorder the terms:
(9 + 7D)(D + 7) = 47

Reorder the terms:
(9 + 7D)(7 + D) = 47

Multiply (9 + 7D) * (7 + D)
(9(7 + D) + 7D * (7 + D)) = 47
((7 * 9 + D * 9) + 7D * (7 + D)) = 47
((63 + 9D) + 7D * (7 + D)) = 47
(63 + 9D + (7 * 7D + D * 7D)) = 47
(63 + 9D + (49D + 7D2)) = 47

Combine like terms: 9D + 49D = 58D
(63 + 58D + 7D2) = 47

Solving
63 + 58D + 7D2 = 47

Solving for variable 'D'.

Reorder the terms:
63 + -47 + 58D + 7D2 = 47 + -47

Combine like terms: 63 + -47 = 16
16 + 58D + 7D2 = 47 + -47

Combine like terms: 47 + -47 = 0
16 + 58D + 7D2 = 0

Factor a trinomial.
(8 + D)(2 + 7D) = 0


Subproblem 1
Set the factor '(8 + D)' equal to zero and attempt to solve:

Simplifying
8 + D = 0

Solving
8 + D = 0

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

Add '-8' to each side of the equation.
8 + -8 + D = 0 + -8

Combine like terms: 8 + -8 = 0
0 + D = 0 + -8
D = 0 + -8

Combine like terms: 0 + -8 = -8
D = -8

Simplifying
D = -8

Subproblem 2
Set the factor '(2 + 7D)' equal to zero and attempt to solve:

Simplifying
2 + 7D = 0

Solving
2 + 7D = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7D = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7D = 0 + -2
7D = 0 + -2

Combine like terms: 0 + -2 = -2
7D = -2

Divide each side by '7'.
D = -0.2857142857

Simplifying
D = -0.2857142857
Solution
D = {-8, -0.2857142857}

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