4d(d+1)+13=5(d^2+4)-4d

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Solution for 4d(d+1)+13=5(d^2+4)-4d equation: 


Simplifying
4d(d + 1) + 13 = 5(d2 + 4) + -4d

Reorder the terms:
4d(1 + d) + 13 = 5(d2 + 4) + -4d
(1 * 4d + d * 4d) + 13 = 5(d2 + 4) + -4d
(4d + 4d2) + 13 = 5(d2 + 4) + -4d

Reorder the terms:
13 + 4d + 4d2 = 5(d2 + 4) + -4d

Reorder the terms:
13 + 4d + 4d2 = 5(4 + d2) + -4d
13 + 4d + 4d2 = (4 * 5 + d2 * 5) + -4d
13 + 4d + 4d2 = (20 + 5d2) + -4d

Reorder the terms:
13 + 4d + 4d2 = 20 + -4d + 5d2

Solving
13 + 4d + 4d2 = 20 + -4d + 5d2

Solving for variable 'd'.

Reorder the terms:
13 + -20 + 4d + 4d + 4d2 + -5d2 = 20 + -4d + 5d2 + -20 + 4d + -5d2

Combine like terms: 13 + -20 = -7
-7 + 4d + 4d + 4d2 + -5d2 = 20 + -4d + 5d2 + -20 + 4d + -5d2

Combine like terms: 4d + 4d = 8d
-7 + 8d + 4d2 + -5d2 = 20 + -4d + 5d2 + -20 + 4d + -5d2

Combine like terms: 4d2 + -5d2 = -1d2
-7 + 8d + -1d2 = 20 + -4d + 5d2 + -20 + 4d + -5d2

Reorder the terms:
-7 + 8d + -1d2 = 20 + -20 + -4d + 4d + 5d2 + -5d2

Combine like terms: 20 + -20 = 0
-7 + 8d + -1d2 = 0 + -4d + 4d + 5d2 + -5d2
-7 + 8d + -1d2 = -4d + 4d + 5d2 + -5d2

Combine like terms: -4d + 4d = 0
-7 + 8d + -1d2 = 0 + 5d2 + -5d2
-7 + 8d + -1d2 = 5d2 + -5d2

Combine like terms: 5d2 + -5d2 = 0
-7 + 8d + -1d2 = 0

Factor a trinomial.
(-7 + d)(1 + -1d) = 0


Subproblem 1
Set the factor '(-7 + d)' equal to zero and attempt to solve:

Simplifying
-7 + d = 0

Solving
-7 + d = 0

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

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

Combine like terms: -7 + 7 = 0
0 + d = 0 + 7
d = 0 + 7

Combine like terms: 0 + 7 = 7
d = 7

Simplifying
d = 7

Subproblem 2
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
Solution
d = {7, 1}

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