Solve (2x-3)(x-1)-4(x-5)(x^3)

Question

Simplify the expression

2 x^{2} - 5 x + 3 - 4 x^{4} + 20 x^{3}

Evaluate

(2 x - 3) (x - 1) - 4 (x - 5) x^{3}

Multiply the terms

(2 x - 3) (x - 1) - 4 x^{3} (x - 5)

Expand the expression

More Steps

Calculate

(2 x - 3) (x - 1)

Apply the distributive property

2 x \times x - 2 x \times 1 - 3 x - (- 3 \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

2 x^{2} - 2 x - 3 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

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

Subtract the terms

More Steps

Evaluate

- 2 x - 3 x

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

(- 2 - 3) x

Subtract the numbers

- 5 x

2 x^{2} - 5 x + 3

2 x^{2} - 5 x + 3 - 4 x^{3} (x - 5)

Solution

More Steps

Calculate

- 4 x^{3} (x - 5)

Apply the distributive property

- 4 x^{3} \times x - (- 4 x^{3} \times 5)

Multiply the terms

More Steps

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}

- 4 x^{4} - (- 4 x^{3} \times 5)

Multiply the numbers

- 4 x^{4} - (- 20 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

- 4 x^{4} + 20 x^{3}

2 x^{2} - 5 x + 3 - 4 x^{4} + 20 x^{3}

Show Solution

Find the roots

x_{1} \approx - 0.687119, x_{2} \approx 5.055797

Evaluate

(2 x - 3) (x - 1) - 4 (x - 5) (x^{3})

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

(2 x - 3) (x - 1) - 4 (x - 5) (x^{3}) = 0

Calculate

(2 x - 3) (x - 1) - 4 (x - 5) x^{3} = 0

Multiply the terms

(2 x - 3) (x - 1) - 4 x^{3} (x - 5) = 0

Calculate

More Steps

Evaluate

(2 x - 3) (x - 1) - 4 x^{3} (x - 5)

Expand the expression

More Steps

Calculate

(2 x - 3) (x - 1)

Apply the distributive property

2 x \times x - 2 x \times 1 - 3 x - (- 3 \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

2 x^{2} - 2 x - 3 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

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

Subtract the terms

2 x^{2} - 5 x + 3

2 x^{2} - 5 x + 3 - 4 x^{3} (x - 5)

Expand the expression

More Steps

Calculate

- 4 x^{3} (x - 5)

Apply the distributive property

- 4 x^{3} \times x - (- 4 x^{3} \times 5)

Multiply the terms

- 4 x^{4} - (- 4 x^{3} \times 5)

Multiply the numbers

- 4 x^{4} - (- 20 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

- 4 x^{4} + 20 x^{3}

2 x^{2} - 5 x + 3 - 4 x^{4} + 20 x^{3}

2 x^{2} - 5 x + 3 - 4 x^{4} + 20 x^{3} = 0

Calculate

x \approx - 0.687119 x \approx 5.055797

Solution

x_{1} \approx - 0.687119, x_{2} \approx 5.055797

Show Solution