4d^2y+7dy-2y=0

Solution for 4d^2y+7dy-2y=0 equation:

Simplifying
4d2y + 7dy + -2y = 0

Reorder the terms:
7dy + 4d2y + -2y = 0

Solving
7dy + 4d2y + -2y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(7d + 4d2 + -2) = 0

Factor a trinomial.
y((4d + -1)(d + 2)) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4d + -1)' equal to zero and attempt to solve:

Simplifying
4d + -1 = 0

Reorder the terms:
-1 + 4d = 0

Solving
-1 + 4d = 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 + 4d = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4d = 0 + 1
4d = 0 + 1

Combine like terms: 0 + 1 = 1
4d = 1

Divide each side by '4'.
d = 0.25

Simplifying
d = 0.25
Subproblem 3
Set the factor '(d + 2)' equal to zero and attempt to solve:

Simplifying
d + 2 = 0

Reorder the terms:
2 + d = 0

Solving
2 + d = 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 + d = 0 + -2

Combine like terms: 2 + -2 = 0
0 + d = 0 + -2
d = 0 + -2

Combine like terms: 0 + -2 = -2
d = -2

Simplifying
d = -2
Solution
d = {0.25, -2}