What are the solutions to the equation 4x^3-6x^2=10x-15 ?

The solutions to the equation 4x^3-6x^2=10x-15 are x= 3/2 ,x=-sqrt(5/2),x=sqrt(5/2)

Find the zeros of 4x^3-6x^2=10x-15

The zeros of 4x^3-6x^2=10x-15 are x= 3/2 ,x=-sqrt(5/2),x=sqrt(5/2)

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4 x^{3} - 6 x^{2} = 10 x - 15

x = \frac{3}{2}, x = - \frac{5}{2}, x = \frac{5}{2}

Decimal Notation

x = 1.5, x = - 1.58113 \dots, x = 1.58113 \dots

Solution steps

4 x^{3} - 6 x^{2} = 10 x - 15

Move

15

to the left side

4 x^{3} - 6 x^{2} + 15 = 10 x

Move

10 x

to the left side

4 x^{3} - 6 x^{2} + 15 - 10 x = 0

Write in the standard form

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

4 x^{3} - 6 x^{2} - 10 x + 15 = 0

Factor

4 x^{3} - 6 x^{2} - 10 x + 15 : (2 x - 3) (2 x + 5) (2 x - 5)

(2 x - 3) (2 x + 5) (2 x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 3 = 0 or 2 x + 5 = 0 or 2 x - 5 = 0

Solve

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

Solve

2 x + 5 = 0 : x = - \frac{5}{2}

Solve

2 x - 5 = 0 : x = \frac{5}{2}

The solutions are

x = \frac{3}{2}, x = - \frac{5}{2}, x = \frac{5}{2}

- 2 x (x^{2} - 5) (x^{2} + 1) = 0

x (x^{2} - 3)^{3} - 2 = 1785

\frac{3}{16} = 3 r^{4}

x^{4} - 7 x^{2} - 5 = 0

2 x^{3} + 5 x + 7 = 0

What are the solutions to the equation 4x^3-6x^2=10x-15 ?
The solutions to the equation 4x^3-6x^2=10x-15 are x= 3/2 ,x=-sqrt(5/2),x=sqrt(5/2)
Find the zeros of 4x^3-6x^2=10x-15
The zeros of 4x^3-6x^2=10x-15 are x= 3/2 ,x=-sqrt(5/2),x=sqrt(5/2)