What are the solutions to the equation 2x^3+32=8x^2+8x ?

The solutions to the equation 2x^3+32=8x^2+8x are x=4,x=-2,x=2

Find the zeros of 2x^3+32=8x^2+8x

The zeros of 2x^3+32=8x^2+8x are x=4,x=-2,x=2

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2 x^{3} + 32 = 8 x^{2} + 8 x

x = 4, x = - 2, x = 2

Solution steps

2 x^{3} + 32 = 8 x^{2} + 8 x

Move

8 x

to the left side

2 x^{3} + 32 - 8 x = 8 x^{2}

Move

8 x^{2}

to the left side

2 x^{3} + 32 - 8 x - 8 x^{2} = 0

Write in the standard form

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

2 x^{3} - 8 x^{2} - 8 x + 32 = 0

Factor

2 x^{3} - 8 x^{2} - 8 x + 32 : 2 (x - 4) (x + 2) (x - 2)

2 (x - 4) (x + 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x + 2 = 0 or x - 2 = 0

Solve

x - 4 = 0 : x = 4

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = 4, x = - 2, x = 2

(x) = 3 x^{3} - 12 x^{2} + 8 x + 2

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

x^{3} - 5 = - 7

x^{4} - 8 x^{2} + 9 = 0

6 x^{3} - 12 x^{2} + 6 x = 0

What are the solutions to the equation 2x^3+32=8x^2+8x ?
The solutions to the equation 2x^3+32=8x^2+8x are x=4,x=-2,x=2
Find the zeros of 2x^3+32=8x^2+8x
The zeros of 2x^3+32=8x^2+8x are x=4,x=-2,x=2