20d^4-68d^3+24d^2=

Solution for 20d^4-68d^3+24d^2= equation:

Simplifying
20d4 + -68d3 + 24d2 = 0

Reorder the terms:
24d2 + -68d3 + 20d4 = 0

Solving
24d2 + -68d3 + 20d4 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '4d2'.
4d2(6 + -17d + 5d2) = 0

Factor a trinomial.
4d2((2 + -5d)(3 + -1d)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'd2' equal to zero and attempt to solve:

Simplifying
d2 = 0

Solving
d2 = 0

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

Simplifying
d2 = 0

Take the square root of each side:
d = {0}
Subproblem 2
Set the factor '(2 + -5d)' equal to zero and attempt to solve:

Simplifying
2 + -5d = 0

Solving
2 + -5d = 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 + -5d = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5d = 0 + -2
-5d = 0 + -2

Combine like terms: 0 + -2 = -2
-5d = -2

Divide each side by '-5'.
d = 0.4

Simplifying
d = 0.4
Subproblem 3
Set the factor '(3 + -1d)' equal to zero and attempt to solve:

Simplifying
3 + -1d = 0

Solving
3 + -1d = 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 + -1d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1d = 0 + -3
-1d = 0 + -3

Combine like terms: 0 + -3 = -3
-1d = -3

Divide each side by '-1'.
d = 3

Simplifying
d = 3
Solution
d = {0, 0.4, 3}