Solve (2x^6) (3x^2 4x-7)

Question

Simplify the expression

24 x^{9} - 14 x^{6}

Evaluate

2 x^{6} (3 x^{2} \times 4 x - 7)

Multiply

More Steps

Evaluate

3 x^{2} \times 4 x

Multiply the terms

12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

12 x^{2 + 1}

Add the numbers

12 x^{3}

2 x^{6} (12 x^{3} - 7)

Apply the distributive property

2 x^{6} \times 12 x^{3} - 2 x^{6} \times 7

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

24 x^{6} \times x^{3}

Multiply the terms

More Steps

Evaluate

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

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

x^{6 + 3}

Add the numbers

x^{9}

24 x^{9}

24 x^{9} - 2 x^{6} \times 7

Solution

24 x^{9} - 14 x^{6}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 126}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.83555

Evaluate

(2 x^{6}) (3 x^{2} \times 4 x - 7)

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

(2 x^{6}) (3 x^{2} \times 4 x - 7) = 0

Multiply the terms

2 x^{6} (3 x^{2} \times 4 x - 7) = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 4 x

Multiply the terms

12 x^{2} \times x

Multiply the terms with the same base by adding their exponents

12 x^{2 + 1}

Add the numbers

12 x^{3}

2 x^{6} (12 x^{3} - 7) = 0

Elimination the left coefficient

x^{6} (12 x^{3} - 7) = 0

Separate the equation into 2 possible cases

x^{6} = 0 12 x^{3} - 7 = 0

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

x = 0 12 x^{3} - 7 = 0

Solve the equation

More Steps

Evaluate

12 x^{3} - 7 = 0

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

12 x^{3} = 0 + 7

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

12 x^{3} = 7

Divide both sides

\frac{12 x ^{3}}{12} = \frac{7}{12}

Divide the numbers

x^{3} = \frac{7}{12}

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

3 x^{3} = 3 \frac{7}{12}

Calculate

x = 3 \frac{7}{12}

Simplify the root

More Steps

Evaluate

3 \frac{7}{12}

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

\frac{3 7}{3 12}

Multiply by the Conjugate

\frac{3 7 \times 3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{3 7 \times 2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

\frac{2 3 126}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

\frac{2 3 126}{12}

Cancel out the common factor 2

\frac{3 126}{6}

x = \frac{3 126}{6}

x = 0 x = \frac{3 126}{6}

Solution

x_{1} = 0, x_{2} = \frac{3 126}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.83555

Show Solution