Solve (x 1)(3x^2 10x-6)

Question

Simplify the expression

30 x^{4} - 6 x

Evaluate

(x \times 1) (3 x^{2} \times 10 x - 6)

Remove the parentheses

x \times 1 \times (3 x^{2} \times 10 x - 6)

Multiply

More Steps

Multiply the terms

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

x \times 1 \times (30 x^{3} - 6)

Multiply the terms

x (30 x^{3} - 6)

Apply the distributive property

x \times 30 x^{3} - x \times 6

Multiply the terms

More Steps

Evaluate

x \times 30 x^{3}

Use the commutative property to reorder the terms

30 x \times x^{3}

Multiply the terms

More Steps

Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

30 x^{4}

30 x^{4} - x \times 6

Solution

30 x^{4} - 6 x

Show Solution

Factor the expression

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

Evaluate

(x \times 1) (3 x^{2} \times 10 x - 6)

Remove the parentheses

x \times 1 \times (3 x^{2} \times 10 x - 6)

Multiply

More Steps

Multiply the terms

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

x \times 1 \times (30 x^{3} - 6)

Any expression multiplied by 1 remains the same

x (30 x^{3} - 6)

Factor the expression

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

Solution

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 25}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.584804

Evaluate

(x \times 1) (3 x^{2} \times 10 x - 6)

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

(x \times 1) (3 x^{2} \times 10 x - 6) = 0

Any expression multiplied by 1 remains the same

x (3 x^{2} \times 10 x - 6) = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

x (30 x^{3} - 6) = 0

Separate the equation into 2 possible cases

x = 0 30 x^{3} - 6 = 0

Solve the equation

More Steps

Evaluate

30 x^{3} - 6 = 0

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

30 x^{3} = 0 + 6

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

30 x^{3} = 6

Divide both sides

\frac{30 x ^{3}}{30} = \frac{6}{30}

Divide the numbers

x^{3} = \frac{6}{30}

Cancel out the common factor 6

x^{3} = \frac{1}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{5}

Calculate

x = 3 \frac{1}{5}

Simplify the root

More Steps

Evaluate

3 \frac{1}{5}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 5}

Simplify the radical expression

\frac{1}{3 5}

Multiply by the Conjugate

\frac{3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 25}{5}

x = \frac{3 25}{5}

x = 0 x = \frac{3 25}{5}

Solution

x_{1} = 0, x_{2} = \frac{3 25}{5}

Alternative Form

x_{1} = 0, x_{2} \approx 0.584804

Show Solution