What are the solutions to the equation x^4+2x^3=5x^2+6x ?

The solutions to the equation x^4+2x^3=5x^2+6x are x=0,x=-1,x=2,x=-3

Find the zeros of x^4+2x^3=5x^2+6x

The zeros of x^4+2x^3=5x^2+6x are x=0,x=-1,x=2,x=-3

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x^{4} + 2 x^{3} = 5 x^{2} + 6 x

x = 0, x = - 1, x = 2, x = - 3

Solution steps

x^{4} + 2 x^{3} = 5 x^{2} + 6 x

Move

6 x

to the left side

x^{4} + 2 x^{3} - 6 x = 5 x^{2}

Move

5 x^{2}

to the left side

x^{4} + 2 x^{3} - 6 x - 5 x^{2} = 0

Factor

x^{4} + 2 x^{3} - 6 x - 5 x^{2} : x (x + 1) (x - 2) (x + 3)

x (x + 1) (x - 2) (x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 2 = 0 or x + 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

Solve

x + 3 = 0 : x = - 3

The solutions are

x = 0, x = - 1, x = 2, x = - 3

7 x^{3} = 189

x^{3} - 4 x^{2} + x + 6

m^{3} - 6 m^{2} = 0

x^{3} - 9 x^{2} + 24 x - 20 = 0

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

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