Solve (c^2 - 3c^5)(2c^3 c - 6)

Question

Simplify the expression

2 c^{6} - 6 c^{2} - 6 c^{9} + 18 c^{5}

Evaluate

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

Multiply

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Evaluate

2 c^{3} \times c

Multiply the terms with the same base by adding their exponents

2 c^{3 + 1}

Add the numbers

2 c^{4}

(c^{2} - 3 c^{5}) (2 c^{4} - 6)

Apply the distributive property

c^{2} \times 2 c^{4} - c^{2} \times 6 - 3 c^{5} \times 2 c^{4} - (- 3 c^{5} \times 6)

Multiply the terms

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Evaluate

c^{2} \times 2 c^{4}

Use the commutative property to reorder the terms

2 c^{2} \times c^{4}

Multiply the terms

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Evaluate

c^{2} \times c^{4}

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

c^{2 + 4}

Add the numbers

c^{6}

2 c^{6}

2 c^{6} - c^{2} \times 6 - 3 c^{5} \times 2 c^{4} - (- 3 c^{5} \times 6)

Use the commutative property to reorder the terms

2 c^{6} - 6 c^{2} - 3 c^{5} \times 2 c^{4} - (- 3 c^{5} \times 6)

Multiply the terms

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Evaluate

- 3 c^{5} \times 2 c^{4}

Multiply the numbers

- 6 c^{5} \times c^{4}

Multiply the terms

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Evaluate

c^{5} \times c^{4}

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

c^{5 + 4}

Add the numbers

c^{9}

- 6 c^{9}

2 c^{6} - 6 c^{2} - 6 c^{9} - (- 3 c^{5} \times 6)

Multiply the numbers

2 c^{6} - 6 c^{2} - 6 c^{9} - (- 18 c^{5})

Solution

2 c^{6} - 6 c^{2} - 6 c^{9} + 18 c^{5}

Show Solution

Factor the expression

2 c^{2} (1 - 3 c^{3}) (c^{4} - 3)

Evaluate

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

Multiply

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Evaluate

2 c^{3} \times c

Multiply the terms with the same base by adding their exponents

2 c^{3 + 1}

Add the numbers

2 c^{4}

(c^{2} - 3 c^{5}) (2 c^{4} - 6)

Factor the expression

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Evaluate

c^{2} - 3 c^{5}

Rewrite the expression

c^{2} - c^{2} \times 3 c^{3}

Factor out c^{2} from the expression

c^{2} (1 - 3 c^{3})

c^{2} (1 - 3 c^{3}) (2 c^{4} - 6)

Factor the expression

c^{2} (1 - 3 c^{3}) \times 2 (c^{4} - 3)

Solution

2 c^{2} (1 - 3 c^{3}) (c^{4} - 3)

Show Solution

Find the roots

c_{1} = - 43, c_{2} = 0, c_{3} = \frac{3 9}{3}, c_{4} = 43

Alternative Form

c_{1} \approx - 1.316074, c_{2} = 0, c_{3} \approx 0.693361, c_{4} \approx 1.316074

Evaluate

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

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

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

Multiply

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Multiply the terms

2 c^{3} \times c

Multiply the terms with the same base by adding their exponents

2 c^{3 + 1}

Add the numbers

2 c^{4}

(c^{2} - 3 c^{5}) (2 c^{4} - 6) = 0

Separate the equation into 2 possible cases

c^{2} - 3 c^{5} = 0 2 c^{4} - 6 = 0

Solve the equation

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Evaluate

c^{2} - 3 c^{5} = 0

Factor the expression

c^{2} (1 - 3 c^{3}) = 0

Separate the equation into 2 possible cases

c^{2} = 0 1 - 3 c^{3} = 0

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

c = 0 1 - 3 c^{3} = 0

Solve the equation

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Evaluate

1 - 3 c^{3} = 0

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

- 3 c^{3} = 0 - 1

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

- 3 c^{3} = - 1

Change the signs on both sides of the equation

3 c^{3} = 1

Divide both sides

\frac{3 c ^{3}}{3} = \frac{1}{3}

Divide the numbers

c^{3} = \frac{1}{3}

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

3 c^{3} = 3 \frac{1}{3}

Calculate

c = 3 \frac{1}{3}

Simplify the root

c = \frac{3 9}{3}

c = 0 c = \frac{3 9}{3}

c = 0 c = \frac{3 9}{3} 2 c^{4} - 6 = 0

Solve the equation

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Evaluate

2 c^{4} - 6 = 0

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

2 c^{4} = 0 + 6

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

2 c^{4} = 6

Divide both sides

\frac{2 c ^{4}}{2} = \frac{6}{2}

Divide the numbers

c^{4} = \frac{6}{2}

Divide the numbers

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Evaluate

\frac{6}{2}

Reduce the numbers

\frac{3}{1}

Calculate

3

c^{4} = 3

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm 43

Separate the equation into 2 possible cases

c = 43 c = - 43

c = 0 c = \frac{3 9}{3} c = 43 c = - 43

Solution

c_{1} = - 43, c_{2} = 0, c_{3} = \frac{3 9}{3}, c_{4} = 43

Alternative Form

c_{1} \approx - 1.316074, c_{2} = 0, c_{3} \approx 0.693361, c_{4} \approx 1.316074

Show Solution