(3d+7)(5d-6)=0

Solution for (3d+7)(5d-6)=0 equation:

Simplifying
(3d + 7)(5d + -6) = 0

Reorder the terms:
(7 + 3d)(5d + -6) = 0

Reorder the terms:
(7 + 3d)(-6 + 5d) = 0

Multiply (7 + 3d) * (-6 + 5d)
(7(-6 + 5d) + 3d * (-6 + 5d)) = 0
((-6 * 7 + 5d * 7) + 3d * (-6 + 5d)) = 0
((-42 + 35d) + 3d * (-6 + 5d)) = 0
(-42 + 35d + (-6 * 3d + 5d * 3d)) = 0
(-42 + 35d + (-18d + 15d2)) = 0

Combine like terms: 35d + -18d = 17d
(-42 + 17d + 15d2) = 0

Solving
-42 + 17d + 15d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-7 + -3d)(6 + -5d) = 0

Subproblem 1
Set the factor '(-7 + -3d)' equal to zero and attempt to solve:

Simplifying
-7 + -3d = 0

Solving
-7 + -3d = 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 + -3d = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3d = 0 + 7
-3d = 0 + 7

Combine like terms: 0 + 7 = 7
-3d = 7

Divide each side by '-3'.
d = -2.333333333

Simplifying
d = -2.333333333
Subproblem 2
Set the factor '(6 + -5d)' equal to zero and attempt to solve:

Simplifying
6 + -5d = 0

Solving
6 + -5d = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5d = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5d = 0 + -6
-5d = 0 + -6

Combine like terms: 0 + -6 = -6
-5d = -6

Divide each side by '-5'.
d = 1.2

Simplifying
d = 1.2
Solution
d = {-2.333333333, 1.2}