What are the solutions to the equation 3x^3+12x=5x^2+20 ?

The solutions to the equation 3x^3+12x=5x^2+20 are x= 5/3 ,x=2i,x=-2i

Find the zeros of 3x^3+12x=5x^2+20

The zeros of 3x^3+12x=5x^2+20 are x= 5/3 ,x=2i,x=-2i

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3 x^{3} + 12 x = 5 x^{2} + 20

x = \frac{5}{3}, x = 2 i, x = - 2 i

Solution steps

3 x^{3} + 12 x = 5 x^{2} + 20

Move

20

to the left side

3 x^{3} + 12 x - 20 = 5 x^{2}

Move

5 x^{2}

to the left side

3 x^{3} + 12 x - 20 - 5 x^{2} = 0

Write in the standard form

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

3 x^{3} - 5 x^{2} + 12 x - 20 = 0

Factor

3 x^{3} - 5 x^{2} + 12 x - 20 : (3 x - 5) (x^{2} + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 5 = 0 : x = \frac{5}{3}

Solve

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

The solutions are

x = \frac{5}{3}, x = 2 i, x = - 2 i

b^{4} = 16.6

(x + 1) (x^{2} - 4) = 0

x^{4} - 4 x^{3} - 3 x^{2} + 16 x - 4 = 0

x^{3} + 3 x^{2} - 54 x = 0

- 5 x^{4} - 32 = - 12

What are the solutions to the equation 3x^3+12x=5x^2+20 ?
The solutions to the equation 3x^3+12x=5x^2+20 are x= 5/3 ,x=2i,x=-2i
Find the zeros of 3x^3+12x=5x^2+20
The zeros of 3x^3+12x=5x^2+20 are x= 5/3 ,x=2i,x=-2i