What are the solutions to the equation (x-1)(x+1)(x+3)(x+5)+15=0 ?

The solutions to the equation (x-1)(x+1)(x+3)(x+5)+15=0 are x=0,x=-4,x=-2+sqrt(6),x=-2-sqrt(6)

Find the zeros of (x-1)(x+1)(x+3)(x+5)+15=0

The zeros of (x-1)(x+1)(x+3)(x+5)+15=0 are x=0,x=-4,x=-2+sqrt(6),x=-2-sqrt(6)

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(x - 1) (x + 1) (x + 3) (x + 5) + 15 = 0

x = 0, x = - 4, x = - 2 + 6, x = - 2 - 6

Decimal Notation

x = 0, x = - 4, x = 0.44948 \dots, x = - 4.44948 \dots

Solution steps

(x - 1) (x + 1) (x + 3) (x + 5) + 15 = 0

Expand

(x - 1) (x + 1) (x + 3) (x + 5) + 15 : x^{4} + 8 x^{3} + 14 x^{2} - 8 x

x^{4} + 8 x^{3} + 14 x^{2} - 8 x = 0

Factor

x^{4} + 8 x^{3} + 14 x^{2} - 8 x : x (x + 4) (x^{2} + 4 x - 2)

x (x + 4) (x^{2} + 4 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 4 = 0 : x = - 4

Solve

x^{2} + 4 x - 2 = 0 : x = - 2 + 6, x = - 2 - 6

The solutions are

x = 0, x = - 4, x = - 2 + 6, x = - 2 - 6

n^{100} = 2

60 x^{3} - 22 x^{2} - 4 x = 0

x^{3} - 7 x^{2} + 8 x + 10 = 0

x^{4} - 8 x^{9} - 9 = 0

(m^{2} + 1)^{3} (m^{2} + m + 1)^{2} = 0

What are the solutions to the equation (x-1)(x+1)(x+3)(x+5)+15=0 ?
The solutions to the equation (x-1)(x+1)(x+3)(x+5)+15=0 are x=0,x=-4,x=-2+sqrt(6),x=-2-sqrt(6)
Find the zeros of (x-1)(x+1)(x+3)(x+5)+15=0
The zeros of (x-1)(x+1)(x+3)(x+5)+15=0 are x=0,x=-4,x=-2+sqrt(6),x=-2-sqrt(6)