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

Question

Simplify the expression

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

Evaluate

x (x - 3) (2 x - 1)

Multiply the terms

More Steps

Evaluate

x (x - 3)

Apply the distributive property

x \times x - x \times 3

Multiply the terms

x^{2} - x \times 3

Use the commutative property to reorder the terms

x^{2} - 3 x

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

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{2} \times 2 x

Use the commutative property to reorder the terms

2 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

2 x^{3}

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Evaluate

- 3 x \times 2 x

Multiply the numbers

- 6 x \times x

Multiply the terms

- 6 x^{2}

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

Any expression multiplied by 1 remains the same

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

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

Solution

More Steps

Evaluate

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

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

(- 1 - 6) x^{2}

Subtract the numbers

- 7 x^{2}

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{2}, x_{3} = 3

Alternative Form

x_{1} = 0, x_{2} = 0.5, x_{3} = 3

Evaluate

x (x - 3) (2 x - 1)

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

x (x - 3) (2 x - 1) = 0

Separate the equation into 3 possible cases

x = 0 x - 3 = 0 2 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3 2 x - 1 = 0

Solve the equation

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 0 x = 3 x = \frac{1}{2}

Solution

x_{1} = 0, x_{2} = \frac{1}{2}, x_{3} = 3

Alternative Form

x_{1} = 0, x_{2} = 0.5, x_{3} = 3

Show Solution