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

Question

Simplify the expression

21 x^{3} - 6 x^{4} - 9 x^{2}

Evaluate

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

Multiply the first two terms

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

Multiply the terms

More Steps

Evaluate

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}) (3 - x)

Apply the distributive property

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

Multiply the numbers

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

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}

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

Multiply the numbers

18 x^{3} - 6 x^{4} - 9 x^{2} - (- 3 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}

18 x^{3} - 6 x^{4} - 9 x^{2} - (- 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

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

Solution

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Evaluate

18 x^{3} + 3 x^{3}

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

(18 + 3) x^{3}

Add the numbers

21 x^{3}

21 x^{3} - 6 x^{4} - 9 x^{2}

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

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

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

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

Multiply the terms

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

Multiply the first two terms

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

Elimination the left coefficient

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

Separate the equation into 3 possible cases

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

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

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

Solve the equation

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

Solve the equation

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Evaluate

3 - x = 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

Change the signs on both sides of the equation

x = 3

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

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