What are the solutions to the equation 4x^3-12x^2=9x-27 ?

The solutions to the equation 4x^3-12x^2=9x-27 are x=3,x=-3/2 ,x= 3/2

Find the zeros of 4x^3-12x^2=9x-27

The zeros of 4x^3-12x^2=9x-27 are x=3,x=-3/2 ,x= 3/2

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4 x^{3} - 12 x^{2} = 9 x - 27

x = 3, x = - \frac{3}{2}, x = \frac{3}{2}

Decimal Notation

x = 3, x = - 1.5, x = 1.5

Solution steps

4 x^{3} - 12 x^{2} = 9 x - 27

Move

27

to the left side

4 x^{3} - 12 x^{2} + 27 = 9 x

Move

9 x

to the left side

4 x^{3} - 12 x^{2} + 27 - 9 x = 0

Write in the standard form

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

4 x^{3} - 12 x^{2} - 9 x + 27 = 0

Factor

4 x^{3} - 12 x^{2} - 9 x + 27 : (x - 3) (2 x + 3) (2 x - 3)

(x - 3) (2 x + 3) (2 x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x + 3 = 0 or 2 x - 3 = 0

Solve

x - 3 = 0 : x = 3

Solve

2 x + 3 = 0 : x = - \frac{3}{2}

Solve

2 x - 3 = 0 : x = \frac{3}{2}

The solutions are

x = 3, x = - \frac{3}{2}, x = \frac{3}{2}

- x^{3} + 6 x^{2} + 15 x + 8 = 0

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

2 x^{3} - 8 x^{2} - 24 x = a x (x + b) (x + c)

- 2 x^{3} = 32 x

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

What are the solutions to the equation 4x^3-12x^2=9x-27 ?
The solutions to the equation 4x^3-12x^2=9x-27 are x=3,x=-3/2 ,x= 3/2
Find the zeros of 4x^3-12x^2=9x-27
The zeros of 4x^3-12x^2=9x-27 are x=3,x=-3/2 ,x= 3/2