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

Question

Simplify the expression

6 x^{2} - 18 x - 9 x^{5} + 63 x^{4} - 54 x^{3}

Evaluate

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

Multiply

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Multiply the terms

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

Multiply the terms

9 (x^{2} - 6 x) x^{2} (x - 1)

Multiply the terms

9 x^{2} (x^{2} - 6 x) (x - 1)

6 x (x - 3) - 9 x^{2} (x^{2} - 6 x) (x - 1)

Expand the expression

More Steps

Calculate

6 x (x - 3)

Apply the distributive property

6 x \times x - 6 x \times 3

Multiply the terms

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

Multiply the numbers

6 x^{2} - 18 x

6 x^{2} - 18 x - 9 x^{2} (x^{2} - 6 x) (x - 1)

Solution

More Steps

Calculate

- 9 x^{2} (x^{2} - 6 x) (x - 1)

Simplify

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Evaluate

- 9 x^{2} (x^{2} - 6 x)

Apply the distributive property

- 9 x^{2} \times x^{2} - (- 9 x^{2} \times 6 x)

Multiply the terms

- 9 x^{4} - (- 9 x^{2} \times 6 x)

Multiply the terms

- 9 x^{4} - (- 54 x^{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 9 x^{4} + 54 x^{3}

(- 9 x^{4} + 54 x^{3}) (x - 1)

Apply the distributive property

- 9 x^{4} \times x - (- 9 x^{4} \times 1) + 54 x^{3} \times x - 54 x^{3} \times 1

Multiply the terms

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Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

- 9 x^{5} - (- 9 x^{4} \times 1) + 54 x^{3} \times x - 54 x^{3} \times 1

Any expression multiplied by 1 remains the same

- 9 x^{5} - (- 9 x^{4}) + 54 x^{3} \times x - 54 x^{3} \times 1

Multiply the terms

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Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

- 9 x^{5} - (- 9 x^{4}) + 54 x^{4} - 54 x^{3} \times 1

Any expression multiplied by 1 remains the same

- 9 x^{5} - (- 9 x^{4}) + 54 x^{4} - 54 x^{3}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 9 x^{5} + 9 x^{4} + 54 x^{4} - 54 x^{3}

Add the terms

More Steps

Evaluate

9 x^{4} + 54 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(9 + 54) x^{4}

Add the numbers

63 x^{4}

- 9 x^{5} + 63 x^{4} - 54 x^{3}

6 x^{2} - 18 x - 9 x^{5} + 63 x^{4} - 54 x^{3}

Show Solution

Factor the expression

3 x (2 x - 6 - 3 x^{4} + 21 x^{3} - 18 x^{2})

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

9 (x^{2} - 6 x) x^{2} (x - 1)

Multiply the terms

9 x^{2} (x^{2} - 6 x) (x - 1)

6 x (x - 3) - 9 x^{2} (x^{2} - 6 x) (x - 1)

Rewrite the expression

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

Factor out 3 x from the expression

3 x (2 (x - 3) - 3 x (x^{2} - 6 x) (x - 1))

Solution

3 x (2 x - 6 - 3 x^{4} + 21 x^{3} - 18 x^{2})

Show Solution

Find the roots

x_{1} = 0, x_{2} \approx 1.180576, x_{3} \approx 6.011086

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

9 (x^{2} - 6 x) x^{2} (x - 1)

Multiply the terms

9 x^{2} (x^{2} - 6 x) (x - 1)

6 x (x - 3) - 9 x^{2} (x^{2} - 6 x) (x - 1) = 0

Calculate

More Steps

Evaluate

6 x (x - 3) - 9 x^{2} (x^{2} - 6 x) (x - 1)

Expand the expression

More Steps

Calculate

6 x (x - 3)

Apply the distributive property

6 x \times x - 6 x \times 3

Multiply the terms

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

Multiply the numbers

6 x^{2} - 18 x

6 x^{2} - 18 x - 9 x^{2} (x^{2} - 6 x) (x - 1)

Expand the expression

More Steps

Calculate

- 9 x^{2} (x^{2} - 6 x) (x - 1)

Simplify

(- 9 x^{4} + 54 x^{3}) (x - 1)

Apply the distributive property

- 9 x^{4} \times x - (- 9 x^{4} \times 1) + 54 x^{3} \times x - 54 x^{3} \times 1

Multiply the terms

- 9 x^{5} - (- 9 x^{4} \times 1) + 54 x^{3} \times x - 54 x^{3} \times 1

Any expression multiplied by 1 remains the same

- 9 x^{5} - (- 9 x^{4}) + 54 x^{3} \times x - 54 x^{3} \times 1

Multiply the terms

- 9 x^{5} - (- 9 x^{4}) + 54 x^{4} - 54 x^{3} \times 1

Any expression multiplied by 1 remains the same

- 9 x^{5} - (- 9 x^{4}) + 54 x^{4} - 54 x^{3}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 9 x^{5} + 9 x^{4} + 54 x^{4} - 54 x^{3}

Add the terms

- 9 x^{5} + 63 x^{4} - 54 x^{3}

6 x^{2} - 18 x - 9 x^{5} + 63 x^{4} - 54 x^{3}

6 x^{2} - 18 x - 9 x^{5} + 63 x^{4} - 54 x^{3} = 0

Factor the expression

3 x (2 x - 6 - 3 x^{4} + 21 x^{3} - 18 x^{2}) = 0

Divide both sides

x (2 x - 6 - 3 x^{4} + 21 x^{3} - 18 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 2 x - 6 - 3 x^{4} + 21 x^{3} - 18 x^{2} = 0

Solve the equation

x = 0 x \approx 1.180576 x \approx 6.011086

Solution

x_{1} = 0, x_{2} \approx 1.180576, x_{3} \approx 6.011086

Show Solution