Solve (2x-1)*(3x^2)-6x*(x-1)-7x^4

Question

Simplify the expression

6 x^{3} - 9 x^{2} + 6 x - 7 x^{4}

Evaluate

(2 x - 1) \times 3 x^{2} - 6 x (x - 1) - 7 x^{4}

Multiply the terms

3 x^{2} (2 x - 1) - 6 x (x - 1) - 7 x^{4}

Expand the expression

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Calculate

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

Apply the distributive property

3 x^{2} \times 2 x - 3 x^{2} \times 1

Multiply the terms

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Evaluate

3 x^{2} \times 2 x

Multiply the numbers

6 x^{2} \times x

Multiply the terms

6 x^{3}

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

Any expression multiplied by 1 remains the same

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

6 x^{3} - 3 x^{2} - 6 x (x - 1) - 7 x^{4}

Expand the expression

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Calculate

- 6 x (x - 1)

Apply the distributive property

- 6 x \times x - (- 6 x \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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

- 6 x^{2} + 6 x

6 x^{3} - 3 x^{2} - 6 x^{2} + 6 x - 7 x^{4}

Solution

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Evaluate

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

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

(- 3 - 6) x^{2}

Subtract the numbers

- 9 x^{2}

6 x^{3} - 9 x^{2} + 6 x - 7 x^{4}

Show Solution

Factor the expression

x (6 x^{2} - 9 x + 6 - 7 x^{3})

Evaluate

(2 x - 1) \times 3 x^{2} - 6 x (x - 1) - 7 x^{4}

Multiply the terms

3 x^{2} (2 x - 1) - 6 x (x - 1) - 7 x^{4}

Simplify

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Evaluate

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

Apply the distributive property

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

Multiply the terms

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Evaluate

3 x^{2} \times 2 x

Multiply the numbers

6 x^{2} \times x

Multiply the terms

6 x^{3}

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

Multiply the terms

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

6 x^{3} - 3 x^{2} - 6 x (x - 1) - 7 x^{4}

Simplify

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Evaluate

- 6 x (x - 1)

Apply the distributive property

- 6 x \times x - 6 x (- 1)

Multiply the terms

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

Multiply the terms

- 6 x^{2} + 6 x

6 x^{3} - 3 x^{2} - 6 x^{2} + 6 x - 7 x^{4}

Subtract the terms

More Steps

Evaluate

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

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

(- 3 - 6) x^{2}

Subtract the numbers

- 9 x^{2}

6 x^{3} - 9 x^{2} + 6 x - 7 x^{4}

Rewrite the expression

x \times 6 x^{2} - x \times 9 x + x \times 6 - x \times 7 x^{3}

Solution

x (6 x^{2} - 9 x + 6 - 7 x^{3})

Show Solution

Find the roots

x_{1} = 0, x_{2} \approx 0.721569

Evaluate

(2 x - 1) (3 x^{2}) - 6 x (x - 1) - 7 x^{4}

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

(2 x - 1) (3 x^{2}) - 6 x (x - 1) - 7 x^{4} = 0

Multiply the terms

(2 x - 1) \times 3 x^{2} - 6 x (x - 1) - 7 x^{4} = 0

Multiply the terms

3 x^{2} (2 x - 1) - 6 x (x - 1) - 7 x^{4} = 0

Subtract the terms

More Steps

Simplify

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

Expand the expression

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Calculate

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

Apply the distributive property

3 x^{2} \times 2 x - 3 x^{2} \times 1

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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

Expand the expression

More Steps

Calculate

- 6 x (x - 1)

Apply the distributive property

- 6 x \times x - (- 6 x \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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

- 6 x^{2} + 6 x

6 x^{3} - 3 x^{2} - 6 x^{2} + 6 x

Subtract the terms

More Steps

Evaluate

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

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

(- 3 - 6) x^{2}

Subtract the numbers

- 9 x^{2}

6 x^{3} - 9 x^{2} + 6 x

6 x^{3} - 9 x^{2} + 6 x - 7 x^{4} = 0

Factor the expression

x (6 x^{2} - 9 x + 6 - 7 x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 6 x^{2} - 9 x + 6 - 7 x^{3} = 0

Solve the equation

x = 0 x \approx 0.721569

Solution

x_{1} = 0, x_{2} \approx 0.721569

Show Solution