What are the solutions to the equation x(x+2)(x+4)(x+6)=3465 ?

The solutions to the equation x(x+2)(x+4)(x+6)=3465 are x=5,x=-11,x=-3+3sqrt(6)i,x=-3-3sqrt(6)i

Find the zeros of x(x+2)(x+4)(x+6)=3465

The zeros of x(x+2)(x+4)(x+6)=3465 are x=5,x=-11,x=-3+3sqrt(6)i,x=-3-3sqrt(6)i

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x (x + 2) (x + 4) (x + 6) = 3465

x = 5, x = - 11, x = - 3 + 36 i, x = - 3 - 36 i

Solution steps

x (x + 2) (x + 4) (x + 6) = 3465

Expand

x (x + 2) (x + 4) (x + 6) : x^{4} + 12 x^{3} + 44 x^{2} + 48 x

x^{4} + 12 x^{3} + 44 x^{2} + 48 x = 3465

Move

3465

to the left side

x^{4} + 12 x^{3} + 44 x^{2} + 48 x - 3465 = 0

Factor

x^{4} + 12 x^{3} + 44 x^{2} + 48 x - 3465 : (x - 5) (x + 11) (x^{2} + 6 x + 63)

(x - 5) (x + 11) (x^{2} + 6 x + 63) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x + 11 = 0 or x^{2} + 6 x + 63 = 0

Solve

x - 5 = 0 : x = 5

Solve

x + 11 = 0 : x = - 11

Solve

x^{2} + 6 x + 63 = 0 : x = - 3 + 36 i, x = - 3 - 36 i

The solutions are

x = 5, x = - 11, x = - 3 + 36 i, x = - 3 - 36 i

16 x^{3} + 96 x^{2} - x - 6 = 0

x^{4} + x^{3} + 4 x + 4 = 0

20 = x^{3} + 4 x^{2} - 5 x

x^{3} - 343 = 0

(x - 1)^{3} + 8 = 0

What are the solutions to the equation x(x+2)(x+4)(x+6)=3465 ?
The solutions to the equation x(x+2)(x+4)(x+6)=3465 are x=5,x=-11,x=-3+3sqrt(6)i,x=-3-3sqrt(6)i
Find the zeros of x(x+2)(x+4)(x+6)=3465
The zeros of x(x+2)(x+4)(x+6)=3465 are x=5,x=-11,x=-3+3sqrt(6)i,x=-3-3sqrt(6)i