What are the solutions to the equation 12x^3-9x^2+4x=3 ?

The solutions to the equation 12x^3-9x^2+4x=3 are x= 3/4 ,x= 1/(sqrt(3))i,x=-1/(sqrt(3))i

Find the zeros of 12x^3-9x^2+4x=3

The zeros of 12x^3-9x^2+4x=3 are x= 3/4 ,x= 1/(sqrt(3))i,x=-1/(sqrt(3))i

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12 x^{3} - 9 x^{2} + 4 x = 3

x = \frac{3}{4}, x = \frac{1}{3} i, x = - \frac{1}{3} i

Solution steps

12 x^{3} - 9 x^{2} + 4 x = 3

Move

3

to the left side

12 x^{3} - 9 x^{2} + 4 x - 3 = 0

Factor

12 x^{3} - 9 x^{2} + 4 x - 3 : (4 x - 3) (3 x^{2} + 1)

(4 x - 3) (3 x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

4 x - 3 = 0 or 3 x^{2} + 1 = 0

Solve

4 x - 3 = 0 : x = \frac{3}{4}

Solve

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

The solutions are

x = \frac{3}{4}, x = \frac{1}{3} i, x = - \frac{1}{3} i

x^{4} - 6 x^{3} + 9 x^{2} + 4 x - 12 = 0

y, x^{3} = y^{3}

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

- 4 x^{4} + 4 x^{2} - 1 = 0

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

What are the solutions to the equation 12x^3-9x^2+4x=3 ?
The solutions to the equation 12x^3-9x^2+4x=3 are x= 3/4 ,x= 1/(sqrt(3))i,x=-1/(sqrt(3))i
Find the zeros of 12x^3-9x^2+4x=3
The zeros of 12x^3-9x^2+4x=3 are x= 3/4 ,x= 1/(sqrt(3))i,x=-1/(sqrt(3))i