What are the solutions to the equation x^3+5x^2=4x+20 ?

The solutions to the equation x^3+5x^2=4x+20 are x=-5,x=-2,x=2

Find the zeros of x^3+5x^2=4x+20

The zeros of x^3+5x^2=4x+20 are x=-5,x=-2,x=2

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

x = - 5, x = - 2, x = 2

Solution steps

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

Move

20

to the left side

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

Move

4 x

to the left side

x^{3} + 5 x^{2} - 20 - 4 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + 5 x^{2} - 4 x - 20 = 0

Factor

x^{3} + 5 x^{2} - 4 x - 20 : (x + 5) (x + 2) (x - 2)

(x + 5) (x + 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 5 = 0 or x + 2 = 0 or x - 2 = 0

Solve

x + 5 = 0 : x = - 5

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = - 5, x = - 2, x = 2

x^{4} + 62 x^{2} + 128 x + 65

a^{4} + a^{3} + a^{2} + a + 1 = 0

x^{4} - 113 x^{2} + 3136 = 0

x^{4} - 3 x^{3} - 5 x^{2} + 6 x - 8

m^{5} - m = 0

What are the solutions to the equation x^3+5x^2=4x+20 ?
The solutions to the equation x^3+5x^2=4x+20 are x=-5,x=-2,x=2
Find the zeros of x^3+5x^2=4x+20
The zeros of x^3+5x^2=4x+20 are x=-5,x=-2,x=2