(d-5)(4d)+(d-5)(d+7)=0

Solution for (d-5)(4d)+(d-5)(d+7)=0 equation:

Simplifying
(d + -5)(4d) + (d + -5)(d + 7) = 0

Reorder the terms:
(-5 + d)(4d) + (d + -5)(d + 7) = 0

Remove parenthesis around (4d)
(-5 + d) * 4d + (d + -5)(d + 7) = 0

Reorder the terms for easier multiplication:
4d(-5 + d) + (d + -5)(d + 7) = 0
(-5 * 4d + d * 4d) + (d + -5)(d + 7) = 0
(-20d + 4d2) + (d + -5)(d + 7) = 0

Reorder the terms:
-20d + 4d2 + (-5 + d)(d + 7) = 0

Reorder the terms:
-20d + 4d2 + (-5 + d)(7 + d) = 0

Multiply (-5 + d) * (7 + d)
-20d + 4d2 + (-5(7 + d) + d(7 + d)) = 0
-20d + 4d2 + ((7 * -5 + d * -5) + d(7 + d)) = 0
-20d + 4d2 + ((-35 + -5d) + d(7 + d)) = 0
-20d + 4d2 + (-35 + -5d + (7 * d + d * d)) = 0
-20d + 4d2 + (-35 + -5d + (7d + d2)) = 0

Combine like terms: -5d + 7d = 2d
-20d + 4d2 + (-35 + 2d + d2) = 0

Reorder the terms:
-35 + -20d + 2d + 4d2 + d2 = 0

Combine like terms: -20d + 2d = -18d
-35 + -18d + 4d2 + d2 = 0

Combine like terms: 4d2 + d2 = 5d2
-35 + -18d + 5d2 = 0

Solving
-35 + -18d + 5d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-7 + -5d)(5 + -1d) = 0

Subproblem 1
Set the factor '(-7 + -5d)' equal to zero and attempt to solve:

Simplifying
-7 + -5d = 0

Solving
-7 + -5d = 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 + -5d = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5d = 0 + 7
-5d = 0 + 7

Combine like terms: 0 + 7 = 7
-5d = 7

Divide each side by '-5'.
d = -1.4

Simplifying
d = -1.4
Subproblem 2
Set the factor '(5 + -1d)' equal to zero and attempt to solve:

Simplifying
5 + -1d = 0

Solving
5 + -1d = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1d = 0 + -5
-1d = 0 + -5

Combine like terms: 0 + -5 = -5
-1d = -5

Divide each side by '-1'.
d = 5

Simplifying
d = 5
Solution
d = {-1.4, 5}