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

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

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

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

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

x = 2, x = - 2

Solution steps

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

Move

6

to the left side

x^{3} - 2 x^{2} + 8 = 4 x

Move

4 x

to the left side

x^{3} - 2 x^{2} + 8 - 4 x = 0

Write in the standard form

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

x^{3} - 2 x^{2} - 4 x + 8 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x + 2 = 0

Solve

x - 2 = 0 : x = 2

Solve

x + 2 = 0 : x = - 2

The solutions are

x = 2, x = - 2

5 x^{5} - 30 x^{4} + 45 x^{3} = 0

75 y^{3} + 100 y^{2} - 3 y - 4 = 0

36 x^{3} + 24 x^{2} + 4 x = 0

925 = 5 x^{3}

x^{3} = - 12

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