What are the solutions to the equation 5x-6=2x^3-3x^2 ?

The solutions to the equation 5x-6=2x^3-3x^2 are x=1,x=-3/2 ,x=2

Find the zeros of 5x-6=2x^3-3x^2

The zeros of 5x-6=2x^3-3x^2 are x=1,x=-3/2 ,x=2

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

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

Decimal Notation

x = 1, x = - 1.5, x = 2

Solution steps

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

Switch sides

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

Move

6

to the left side

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

Move

5 x

to the left side

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

Write in the standard form

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

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

Factor

2 x^{3} - 3 x^{2} - 5 x + 6 : (x - 1) (2 x + 3) (x - 2)

(x - 1) (2 x + 3) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 2 x + 3 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

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

Solve

x - 2 = 0 : x = 2

The solutions are

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

(3 x - 2)^{5} = 24

(2 + b) (11 b - 2 b^{2}) + 189 = 0

x, x^{4} y^{3} - 2 x y^{4} = x y^{3}

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

x^{3} - 5 x^{2} + 9 x - 45 = 0

What are the solutions to the equation 5x-6=2x^3-3x^2 ?
The solutions to the equation 5x-6=2x^3-3x^2 are x=1,x=-3/2 ,x=2
Find the zeros of 5x-6=2x^3-3x^2
The zeros of 5x-6=2x^3-3x^2 are x=1,x=-3/2 ,x=2