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

Question

Simplify the expression

- x^{3} + 5 x^{2} - 6 x

Evaluate

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

Multiply the terms

More Steps

Evaluate

- x (x - 2)

Apply the distributive property

- x \times x - (- x \times 2)

Multiply the terms

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

Use the commutative property to reorder the terms

- x^{2} - (- 2 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

- x^{2} + 2 x

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

Apply the distributive property

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

Multiply the terms

More Steps

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}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

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

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

Solution

More Steps

Evaluate

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

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

(3 + 2) x^{2}

Add the numbers

5 x^{2}

- x^{3} + 5 x^{2} - 6 x

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Find the roots

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

Evaluate

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

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

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

Change the sign

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

Separate the equation into 3 possible cases

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

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

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

Solution

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

Show Solution