(4d-3)(d+6)=0

Solution for (4d-3)(d+6)=0 equation:

Simplifying
(4d + -3)(d + 6) = 0

Reorder the terms:
(-3 + 4d)(d + 6) = 0

Reorder the terms:
(-3 + 4d)(6 + d) = 0

Multiply (-3 + 4d) * (6 + d)
(-3(6 + d) + 4d * (6 + d)) = 0
((6 * -3 + d * -3) + 4d * (6 + d)) = 0
((-18 + -3d) + 4d * (6 + d)) = 0
(-18 + -3d + (6 * 4d + d * 4d)) = 0
(-18 + -3d + (24d + 4d2)) = 0

Combine like terms: -3d + 24d = 21d
(-18 + 21d + 4d2) = 0

Solving
-18 + 21d + 4d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-6 + -1d)(3 + -4d) = 0

Subproblem 1
Set the factor '(-6 + -1d)' equal to zero and attempt to solve:

Simplifying
-6 + -1d = 0

Solving
-6 + -1d = 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 + -1d = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1d = 0 + 6
-1d = 0 + 6

Combine like terms: 0 + 6 = 6
-1d = 6

Divide each side by '-1'.
d = -6

Simplifying
d = -6
Subproblem 2
Set the factor '(3 + -4d)' equal to zero and attempt to solve:

Simplifying
3 + -4d = 0

Solving
3 + -4d = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4d = 0 + -3
-4d = 0 + -3

Combine like terms: 0 + -3 = -3
-4d = -3

Divide each side by '-4'.
d = 0.75

Simplifying
d = 0.75
Solution
d = {-6, 0.75}