What are the solutions to the equation (x+3)(x^2+3x+5)=x^2+3x ?

The solutions to the equation (x+3)(x^2+3x+5)=x^2+3x are x=-3,x=-1+2i,x=-1-2i

Find the zeros of (x+3)(x^2+3x+5)=x^2+3x

The zeros of (x+3)(x^2+3x+5)=x^2+3x are x=-3,x=-1+2i,x=-1-2i

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(x + 3) (x^{2} + 3 x + 5) = x^{2} + 3 x

x = - 3, x = - 1 + 2 i, x = - 1 - 2 i

Solution steps

(x + 3) (x^{2} + 3 x + 5) = x^{2} + 3 x

Expand

(x + 3) (x^{2} + 3 x + 5) : x^{3} + 6 x^{2} + 14 x + 15

x^{3} + 6 x^{2} + 14 x + 15 = x^{2} + 3 x

Move

3 x

to the left side

x^{3} + 6 x^{2} + 11 x + 15 = x^{2}

Move

x^{2}

to the left side

x^{3} + 5 x^{2} + 11 x + 15 = 0

Factor

x^{3} + 5 x^{2} + 11 x + 15 : (x + 3) (x^{2} + 2 x + 5)

(x + 3) (x^{2} + 2 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 = 0 or x^{2} + 2 x + 5 = 0

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} + 2 x + 5 = 0 : x = - 1 + 2 i, x = - 1 - 2 i

The solutions are

x = - 3, x = - 1 + 2 i, x = - 1 - 2 i

x^{3} + 2 x^{2} - 2 x = 0

x^{3} + x^{2} - 36 = 0

5 x^{3} + x^{2} - 45 x - 9 = 0

r, v = \frac{4 π r ^{3}}{3}

x^{3} - 30 x^{2} + 80 x - 400 = 0

What are the solutions to the equation (x+3)(x^2+3x+5)=x^2+3x ?
The solutions to the equation (x+3)(x^2+3x+5)=x^2+3x are x=-3,x=-1+2i,x=-1-2i
Find the zeros of (x+3)(x^2+3x+5)=x^2+3x
The zeros of (x+3)(x^2+3x+5)=x^2+3x are x=-3,x=-1+2i,x=-1-2i