Solve 6x^(3)-27x^(2)-15x

Question

Factor the expression

3 x (x - 5) (2 x + 1)

Evaluate

6 x^{3} - 27 x^{2} - 15 x

Rewrite the expression

3 x \times 2 x^{2} - 3 x \times 9 x - 3 x \times 5

Factor out 3 x from the expression

3 x (2 x^{2} - 9 x - 5)

Solution

More Steps

Evaluate

2 x^{2} - 9 x - 5

Rewrite the expression

2 x^{2} + (1 - 10) x - 5

Calculate

2 x^{2} + x - 10 x - 5

Rewrite the expression

x \times 2 x + x - 5 \times 2 x - 5

Factor out x from the expression

x (2 x + 1) - 5 \times 2 x - 5

Factor out - 5 from the expression

x (2 x + 1) - 5 (2 x + 1)

Factor out 2 x + 1 from the expression

(x - 5) (2 x + 1)

3 x (x - 5) (2 x + 1)

Show Solution

x_{1} = - \frac{1}{2}, x_{2} = 0, x_{3} = 5

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 5

Evaluate

6 x^{3} - 27 x^{2} - 15 x

To find the roots of the expression,set the expression equal to 0

6 x^{3} - 27 x^{2} - 15 x = 0

Factor the expression

3 x (x - 5) (2 x + 1) = 0

Divide both sides

x (x - 5) (2 x + 1) = 0

Separate the equation into 3 possible cases

x = 0 x - 5 = 0 2 x + 1 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

x = 5

x = 0 x = 5 2 x + 1 = 0

Solve the equation

More Steps

Evaluate

2 x + 1 = 0

Move the constant to the right-hand side and change its sign

2 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

2 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{2}

x = 0 x = 5 x = - \frac{1}{2}

Solution

x_{1} = - \frac{1}{2}, x_{2} = 0, x_{3} = 5

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 5

Show Solution