Solve (6x^33x^2-2) (x^3-5x^2-3)

Question

Simplify the expression

18 x^{8} - 90 x^{7} - 54 x^{5} - 2 x^{3} + 10 x^{2} + 6

Evaluate

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

Multiply

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Evaluate

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

Multiply the terms

18 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Apply the distributive property

18 x^{5} \times x^{3} - 18 x^{5} \times 5 x^{2} - 18 x^{5} \times 3 - 2 x^{3} - (- 2 \times 5 x^{2}) - (- 2 \times 3)

Multiply the terms

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Evaluate

x^{5} \times x^{3}

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

x^{5 + 3}

Add the numbers

x^{8}

18 x^{8} - 18 x^{5} \times 5 x^{2} - 18 x^{5} \times 3 - 2 x^{3} - (- 2 \times 5 x^{2}) - (- 2 \times 3)

Multiply the terms

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Evaluate

18 x^{5} \times 5 x^{2}

Multiply the numbers

90 x^{5} \times x^{2}

Multiply the terms

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Evaluate

x^{5} \times x^{2}

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

x^{5 + 2}

Add the numbers

x^{7}

90 x^{7}

18 x^{8} - 90 x^{7} - 18 x^{5} \times 3 - 2 x^{3} - (- 2 \times 5 x^{2}) - (- 2 \times 3)

Multiply the numbers

18 x^{8} - 90 x^{7} - 54 x^{5} - 2 x^{3} - (- 2 \times 5 x^{2}) - (- 2 \times 3)

Multiply the numbers

18 x^{8} - 90 x^{7} - 54 x^{5} - 2 x^{3} - (- 10 x^{2}) - (- 2 \times 3)

Multiply the numbers

18 x^{8} - 90 x^{7} - 54 x^{5} - 2 x^{3} - (- 10 x^{2}) - (- 6)

Solution

18 x^{8} - 90 x^{7} - 54 x^{5} - 2 x^{3} + 10 x^{2} + 6

Show Solution

Factor the expression

2 (9 x^{5} - 1) (x^{3} - 5 x^{2} - 3)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

18 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Solution

2 (9 x^{5} - 1) (x^{3} - 5 x^{2} - 3)

Show Solution

Find the roots

x_{1} = \frac{5 27}{3}, x_{2} \approx 5.114679

Calculate

x_{1} \approx 0.644394, x_{2} \approx 5.114679

Evaluate

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

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

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

Multiply

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Multiply the terms

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

Multiply the terms

18 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

18 x^{3 + 2}

Add the numbers

18 x^{5}

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

Separate the equation into 2 possible cases

18 x^{5} - 2 = 0 x^{3} - 5 x^{2} - 3 = 0

Solve the equation

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Evaluate

18 x^{5} - 2 = 0

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

18 x^{5} = 0 + 2

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

18 x^{5} = 2

Divide both sides

\frac{18 x ^{5}}{18} = \frac{2}{18}

Divide the numbers

x^{5} = \frac{2}{18}

Cancel out the common factor 2

x^{5} = \frac{1}{9}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{9}

Calculate

x = 5 \frac{1}{9}

Simplify the root

More Steps

Evaluate

5 \frac{1}{9}

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

\frac{5 1}{5 9}

Simplify the radical expression

\frac{1}{5 9}

Multiply by the Conjugate

\frac{5 9 ^{4}}{5 9 \times 5 9 ^{4}}

Simplify

\frac{3 5 27}{5 9 \times 5 9 ^{4}}

Multiply the numbers

\frac{3 5 27}{3 ^{2}}

Reduce the fraction

\frac{5 27}{3}

x = \frac{5 27}{3}

x = \frac{5 27}{3} x^{3} - 5 x^{2} - 3 = 0

Solve the equation

x = \frac{5 27}{3} x \approx 5.114679

Solution

x_{1} = \frac{5 27}{3}, x_{2} \approx 5.114679

Calculate

x_{1} \approx 0.644394, x_{2} \approx 5.114679

Show Solution