What are the solutions to the equation 6x^3+13x^2-4=0 ?

The solutions to the equation 6x^3+13x^2-4=0 are x=-2,x= 1/2 ,x=-2/3

Find the zeros of 6x^3+13x^2-4=0

The zeros of 6x^3+13x^2-4=0 are x=-2,x= 1/2 ,x=-2/3

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6 x^{3} + 13 x^{2} - 4 = 0

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

Decimal

x = - 2, x = 0.5, x = - 0.66666 \dots

Solution steps

6 x^{3} + 13 x^{2} - 4 = 0

Factor

6 x^{3} + 13 x^{2} - 4 : (x + 2) (2 x - 1) (3 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

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

The solutions are

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

2 x^{3} - 7 x^{2} - 6 x + 8 = 0

x, x^{4} - 6 x^{2} + 12 = 7

25 x^{4} - 61 x^{2} + 36 = 0

y = x^{3}, x

x^{3} = 49

What are the solutions to the equation 6x^3+13x^2-4=0 ?
The solutions to the equation 6x^3+13x^2-4=0 are x=-2,x= 1/2 ,x=-2/3
Find the zeros of 6x^3+13x^2-4=0
The zeros of 6x^3+13x^2-4=0 are x=-2,x= 1/2 ,x=-2/3