Question

6x^3 - 7x^2 - 3x = 0. Show the correct steps.

Answer 1

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

Explanation:

6x^3 - 7x^2 - 3x = 0

Factor out an x.

x(6x^2 - 7x - 3) = 0

To factor the trinomial, we try trial and error.

6x = 2x * 3x

-3 = -1 * 3 = -3 * 1

We need to place 2x and 3x and -1 and 3 or -3 and 1 in order to make the middle term come out as -7x.

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

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

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

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

Answer 2

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Answer:

x = -1/3, 0, 3/2.

Explanation:

Starting with:

6x³ - 7x² - 3x = 0

Factor out a greatest common factor, or x from each term:

x(6x² - 7x - 3) = 0

Factor the expression inside of the parenthesis:

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

Use the Zero Product Property to find the solutions:

x = 0

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3x + 1 = 0

3x = -1

x = -1/3

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2x - 3 = 0

2x = 3

x = 3/2

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The solutions to this equation are x = -1/3, 0, 3/2.