Solve 2x(x^4) (6x-3)

Question

Simplify the expression

12 x^{6} - 6 x^{5}

Evaluate

2 x \times x^{4} (6 x - 3)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Apply the distributive property

2 x^{5} \times 6 x - 2 x^{5} \times 3

Multiply the terms

More Steps

Evaluate

2 x^{5} \times 6 x

Multiply the numbers

12 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}

12 x^{6}

12 x^{6} - 2 x^{5} \times 3

Solution

12 x^{6} - 6 x^{5}

Show Solution

6 x^{5} (2 x - 1)

Evaluate

2 x \times x^{4} (6 x - 3)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Factor the expression

2 x^{5} \times 3 (2 x - 1)

Solution

6 x^{5} (2 x - 1)

Show Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0.5

Evaluate

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

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

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

Calculate

2 x \times x^{4} (6 x - 3) = 0

Multiply

More Steps

Multiply the terms

2 x \times x^{4} (6 x - 3)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

x^{5} = 0 6 x - 3 = 0

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

x = 0 6 x - 3 = 0

Solve the equation

More Steps

Evaluate

6 x - 3 = 0

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

6 x = 0 + 3

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

6 x = 3

Divide both sides

\frac{6 x}{6} = \frac{3}{6}

Divide the numbers

x = \frac{3}{6}

Cancel out the common factor 3

x = \frac{1}{2}

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

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0.5

Show Solution