What are the solutions to the equation 5d^7=40d^4 ?

The solutions to the equation 5d^7=40d^4 are d=0,d=2,d=-1+sqrt(3)i,d=-1-sqrt(3)i

Find the zeros of 5d^7=40d^4

The zeros of 5d^7=40d^4 are d=0,d=2,d=-1+sqrt(3)i,d=-1-sqrt(3)i

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5 d^{7} = 40 d^{4}

d = 0, d = 2, d = - 1 + 3 i, d = - 1 - 3 i

Solution steps

5 d^{7} = 40 d^{4}

Move

40 d^{4}

to the left side

5 d^{7} - 40 d^{4} = 0

Factor

5 d^{7} - 40 d^{4} : 5 d^{4} (d - 2) (d^{2} + 2 d + 4)

5 d^{4} (d - 2) (d^{2} + 2 d + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

d = 0 or d - 2 = 0 or d^{2} + 2 d + 4 = 0

Solve

d - 2 = 0 : d = 2

Solve

d^{2} + 2 d + 4 = 0 : d = - 1 + 3 i, d = - 1 - 3 i

The solutions are

d = 0, d = 2, d = - 1 + 3 i, d = - 1 - 3 i

x^{3} - 64 = x - 4

x^{4} - 4 x^{3} - 1 = 0

3 x^{3} + 4 = x^{2} + 12 x

8 x^{3} - 6 x - 1 = 0

x^{4} = 64

What are the solutions to the equation 5d^7=40d^4 ?
The solutions to the equation 5d^7=40d^4 are d=0,d=2,d=-1+sqrt(3)i,d=-1-sqrt(3)i
Find the zeros of 5d^7=40d^4
The zeros of 5d^7=40d^4 are d=0,d=2,d=-1+sqrt(3)i,d=-1-sqrt(3)i