What are the solutions to the equation x(x-3)(x-2)=72 ?

The solutions to the equation x(x-3)(x-2)=72 are x=6,x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2

Find the zeros of x(x-3)(x-2)=72

The zeros of x(x-3)(x-2)=72 are x=6,x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2

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x (x - 3) (x - 2) = 72

x = 6, x = - \frac{1}{2} + i \frac{47}{2}, x = - \frac{1}{2} - i \frac{47}{2}

Solution steps

x (x - 3) (x - 2) = 72

Expand

x (x - 3) (x - 2) : x^{3} - 5 x^{2} + 6 x

x^{3} - 5 x^{2} + 6 x = 72

Move

72

to the left side

x^{3} - 5 x^{2} + 6 x - 72 = 0

Factor

x^{3} - 5 x^{2} + 6 x - 72 : (x - 6) (x^{2} + x + 12)

(x - 6) (x^{2} + x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 6 = 0 : x = 6

Solve

x^{2} + x + 12 = 0 : x = - \frac{1}{2} + i \frac{47}{2}, x = - \frac{1}{2} - i \frac{47}{2}

The solutions are

x = 6, x = - \frac{1}{2} + i \frac{47}{2}, x = - \frac{1}{2} - i \frac{47}{2}

x^{3} + x^{2} + x + 1

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

z^{4} = - 1 - i 3

x, 3 x^{3} 0.3 y^{3} + 1 = y

x^{6} + 9 x^{4} + 24 x^{2} + 16 = 0

What are the solutions to the equation x(x-3)(x-2)=72 ?
The solutions to the equation x(x-3)(x-2)=72 are x=6,x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2
Find the zeros of x(x-3)(x-2)=72
The zeros of x(x-3)(x-2)=72 are x=6,x=-1/2+i(sqrt(47))/2 ,x=-1/2-i(sqrt(47))/2