What are the solutions to the equation x^2-4x=x^3-6x^2+8x ?

The solutions to the equation x^2-4x=x^3-6x^2+8x are x=0,x=3,x=4

Find the zeros of x^2-4x=x^3-6x^2+8x

The zeros of x^2-4x=x^3-6x^2+8x are x=0,x=3,x=4

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

x = 0, x = 3, x = 4

Solution steps

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

Switch sides

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

Move

4 x

to the left side

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

Move

x^{2}

to the left side

x^{3} - 7 x^{2} + 12 x = 0

Factor

x^{3} - 7 x^{2} + 12 x : x (x - 3) (x - 4)

x (x - 3) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 3 = 0 or x - 4 = 0

Solve

x - 3 = 0 : x = 3

Solve

x - 4 = 0 : x = 4

The solutions are

x = 0, x = 3, x = 4

s^{3} + s^{2} + 4 s + 4

x^{4} + 8 x^{2} + 12 = 0

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

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

x^{4} + 2 x^{3} + x^{2} + 8 x - 12

What are the solutions to the equation x^2-4x=x^3-6x^2+8x ?
The solutions to the equation x^2-4x=x^3-6x^2+8x are x=0,x=3,x=4
Find the zeros of x^2-4x=x^3-6x^2+8x
The zeros of x^2-4x=x^3-6x^2+8x are x=0,x=3,x=4