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

Question

Simplify the expression

- 2 x^{5} + 12 x^{4}

Evaluate

- x \times 2 x^{3} (x - 6)

Multiply

More Steps

Evaluate

x \times 2 x^{3} (x - 6)

Multiply the terms with the same base by adding their exponents

x^{1 + 3} \times 2 (x - 6)

Add the numbers

x^{4} \times 2 (x - 6)

Use the commutative property to reorder the terms

2 x^{4} (x - 6)

- 2 x^{4} (x - 6)

Apply the distributive property

- 2 x^{4} \times x - (- 2 x^{4} \times 6)

Multiply the terms

More Steps

Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

- 2 x^{5} - (- 2 x^{4} \times 6)

Multiply the numbers

- 2 x^{5} - (- 12 x^{4})

Solution

- 2 x^{5} + 12 x^{4}

Show Solution

x_{1} = 0, x_{2} = 6

Evaluate

- x (2 x^{3}) (x - 6)

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

- x (2 x^{3}) (x - 6) = 0

Multiply the terms

- x \times 2 x^{3} (x - 6) = 0

Multiply

More Steps

Multiply the terms

x \times 2 x^{3} (x - 6)

Multiply the terms with the same base by adding their exponents

x^{1 + 3} \times 2 (x - 6)

Add the numbers

x^{4} \times 2 (x - 6)

Use the commutative property to reorder the terms

2 x^{4} (x - 6)

- 2 x^{4} (x - 6) = 0

Change the sign

2 x^{4} (x - 6) = 0

Elimination the left coefficient

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

Separate the equation into 2 possible cases

x^{4} = 0 x - 6 = 0

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

x = 0 x - 6 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 0 x = 6

Solution

x_{1} = 0, x_{2} = 6

Show Solution