Solve -6x(3x-1)(x^4)

Question

Simplify the expression

- 18 x^{6} + 6 x^{5}

Evaluate

- 6 x (3 x - 1) x^{4}

Multiply the terms with the same base by adding their exponents

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

Add the numbers

- 6 x^{5} (3 x - 1)

Apply the distributive property

- 6 x^{5} \times 3 x - (- 6 x^{5} \times 1)

Multiply the terms

More Steps

Evaluate

- 6 x^{5} \times 3 x

Multiply the numbers

- 18 x^{5} \times x

Multiply the terms

More Steps

Evaluate

x^{5} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{5 + 1}

Add the numbers

x^{6}

- 18 x^{6}

- 18 x^{6} - (- 6 x^{5} \times 1)

Any expression multiplied by 1 remains the same

- 18 x^{6} - (- 6 x^{5})

Solution

- 18 x^{6} + 6 x^{5}

Show Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{3}

Evaluate

- 6 x (3 x - 1) (x^{4})

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

- 6 x (3 x - 1) (x^{4}) = 0

Calculate

- 6 x (3 x - 1) x^{4} = 0

Multiply

More Steps

Multiply the terms

- 6 x (3 x - 1) x^{4}

Multiply the terms with the same base by adding their exponents

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

Add the numbers

- 6 x^{5} (3 x - 1)

- 6 x^{5} (3 x - 1) = 0

Change the sign

6 x^{5} (3 x - 1) = 0

Elimination the left coefficient

x^{5} (3 x - 1) = 0

Separate the equation into 2 possible cases

x^{5} = 0 3 x - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 3 x - 1 = 0

Solve the equation

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = 0 x = \frac{1}{3}

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{3}

Show Solution