What are the solutions to the equation 1-(4-3x)^3=9 ?

The solutions to the equation 1-(4-3x)^3=9 are x=2,x=1+i(sqrt(3))/3 ,x=1-i(sqrt(3))/3

Find the zeros of 1-(4-3x)^3=9

The zeros of 1-(4-3x)^3=9 are x=2,x=1+i(sqrt(3))/3 ,x=1-i(sqrt(3))/3

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1 - (4 - 3 x)^{3} = 9

x = 2, x = 1 + i \frac{3}{3}, x = 1 - i \frac{3}{3}

Solution steps

1 - (4 - 3 x)^{3} = 9

Expand

1 - (4 - 3 x)^{3} : 27 x^{3} - 108 x^{2} + 144 x - 63

27 x^{3} - 108 x^{2} + 144 x - 63 = 9

Move

9

to the left side

27 x^{3} - 108 x^{2} + 144 x - 72 = 0

Factor

27 x^{3} - 108 x^{2} + 144 x - 72 : 9 (x - 2) (3 x^{2} - 6 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

3 x^{2} - 6 x + 4 = 0 : x = 1 + i \frac{3}{3}, x = 1 - i \frac{3}{3}

The solutions are

x = 2, x = 1 + i \frac{3}{3}, x = 1 - i \frac{3}{3}

16 x^{4} - 40 x^{2} + 9 = 0

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

(x + 2) (x + 3) (x + 4) (x + 5) = 195

x^{10} = 0.9

x^{3} + 5 x + 17 = 59

What are the solutions to the equation 1-(4-3x)^3=9 ?
The solutions to the equation 1-(4-3x)^3=9 are x=2,x=1+i(sqrt(3))/3 ,x=1-i(sqrt(3))/3
Find the zeros of 1-(4-3x)^3=9
The zeros of 1-(4-3x)^3=9 are x=2,x=1+i(sqrt(3))/3 ,x=1-i(sqrt(3))/3