Solve (4x^3 -6)(16x^624x^336)

Question

Simplify the expression

55296 x^{12} - 82944 x^{9}

Evaluate

(4 x^{3} - 6) (16 x^{6} \times 24 x^{3} \times 36)

Remove the parentheses

(4 x^{3} - 6) \times 16 x^{6} \times 24 x^{3} \times 36

Multiply the terms

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Evaluate

16 \times 24 \times 36

Multiply the terms

384 \times 36

Multiply the numbers

13824

(4 x^{3} - 6) \times 13824 x^{6} \times x^{3}

Multiply the terms with the same base by adding their exponents

(4 x^{3} - 6) \times 13824 x^{6 + 3}

Add the numbers

(4 x^{3} - 6) \times 13824 x^{9}

Multiply the terms

13824 x^{9} (4 x^{3} - 6)

Apply the distributive property

13824 x^{9} \times 4 x^{3} - 13824 x^{9} \times 6

Multiply the terms

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Evaluate

13824 x^{9} \times 4 x^{3}

Multiply the numbers

55296 x^{9} \times x^{3}

Multiply the terms

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Evaluate

x^{9} \times x^{3}

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

x^{9 + 3}

Add the numbers

x^{12}

55296 x^{12}

55296 x^{12} - 13824 x^{9} \times 6

Solution

55296 x^{12} - 82944 x^{9}

Show Solution

Factor the expression

27648 x^{9} (2 x^{3} - 3)

Evaluate

(4 x^{3} - 6) (16 x^{6} \times 24 x^{3} \times 36)

Remove the parentheses

(4 x^{3} - 6) \times 16 x^{6} \times 24 x^{3} \times 36

Multiply

More Steps

Multiply the terms

16 x^{6} \times 24 x^{3} \times 36

Multiply the terms

More Steps

Evaluate

16 \times 24 \times 36

Multiply the terms

384 \times 36

Multiply the numbers

13824

13824 x^{6} \times x^{3}

Multiply the terms with the same base by adding their exponents

13824 x^{6 + 3}

Add the numbers

13824 x^{9}

(4 x^{3} - 6) \times 13824 x^{9}

Multiply the terms

13824 x^{9} (4 x^{3} - 6)

Factor the expression

13824 x^{9} \times 2 (2 x^{3} - 3)

Solution

27648 x^{9} (2 x^{3} - 3)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 12}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.144714

Evaluate

(4 x^{3} - 6) (16 x^{6} \times 24 x^{3} \times 36)

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

(4 x^{3} - 6) (16 x^{6} \times 24 x^{3} \times 36) = 0

Multiply

More Steps

Multiply the terms

16 x^{6} \times 24 x^{3} \times 36

Multiply the terms

More Steps

Evaluate

16 \times 24 \times 36

Multiply the terms

384 \times 36

Multiply the numbers

13824

13824 x^{6} \times x^{3}

Multiply the terms with the same base by adding their exponents

13824 x^{6 + 3}

Add the numbers

13824 x^{9}

(4 x^{3} - 6) \times 13824 x^{9} = 0

Multiply the terms

13824 x^{9} (4 x^{3} - 6) = 0

Elimination the left coefficient

x^{9} (4 x^{3} - 6) = 0

Separate the equation into 2 possible cases

x^{9} = 0 4 x^{3} - 6 = 0

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

x = 0 4 x^{3} - 6 = 0

Solve the equation

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Evaluate

4 x^{3} - 6 = 0

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

4 x^{3} = 0 + 6

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

4 x^{3} = 6

Divide both sides

\frac{4 x ^{3}}{4} = \frac{6}{4}

Divide the numbers

x^{3} = \frac{6}{4}

Cancel out the common factor 2

x^{3} = \frac{3}{2}

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

3 x^{3} = 3 \frac{3}{2}

Calculate

x = 3 \frac{3}{2}

Simplify the root

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

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

Multiply the numbers

\frac{3 12}{2}

x = \frac{3 12}{2}

x = 0 x = \frac{3 12}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 12}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.144714

Show Solution