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

Question

Simplify the expression

- 15 x^{2} + 99 x - 162

Evaluate

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

Multiply the first two terms

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 3

Multiply the terms

6 \times 3

Multiply the numbers

18

18 (x - 3) (x - 3)

Multiply the terms

18 (x - 3)^{2}

3 (x - 3) x - 18 (x - 3)^{2}

Expand the expression

More Steps

Calculate

3 (x - 3) x

Simplify

More Steps

Evaluate

3 (x - 3)

Apply the distributive property

3 x - 3 \times 3

Multiply the numbers

3 x - 9

(3 x - 9) x

Apply the distributive property

3 x \times x - 9 x

Multiply the terms

3 x^{2} - 9 x

3 x^{2} - 9 x - 18 (x - 3)^{2}

Expand the expression

More Steps

Calculate

- 18 (x - 3)^{2}

Simplify

- 18 (x^{2} - 6 x + 9)

Apply the distributive property

- 18 x^{2} - (- 18 \times 6 x) - 18 \times 9

Multiply the numbers

- 18 x^{2} - (- 108 x) - 18 \times 9

Multiply the numbers

- 18 x^{2} - (- 108 x) - 162

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^{2} + 108 x - 162

3 x^{2} - 9 x - 18 x^{2} + 108 x - 162

Subtract the terms

More Steps

Evaluate

3 x^{2} - 18 x^{2}

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

(3 - 18) x^{2}

Subtract the numbers

- 15 x^{2}

- 15 x^{2} - 9 x + 108 x - 162

Solution

More Steps

Evaluate

- 9 x + 108 x

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

(- 9 + 108) x

Add the numbers

99 x

- 15 x^{2} + 99 x - 162

Show Solution

Factor the expression

3 (x - 3) (- 5 x + 18)

Evaluate

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

Multiply the terms

More Steps

Multiply the terms

(x - 3) \times 3 x

Multiply the first two terms

3 (x - 3) x

Multiply the terms

3 x (x - 3)

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 3

Multiply the terms

6 \times 3

Multiply the numbers

18

18 (x - 3) (x - 3)

Multiply the terms

18 (x - 3)^{2}

3 x (x - 3) - 18 (x - 3)^{2}

Rewrite the expression

3 (x - 3) x - 3 (x - 3) \times 6 (x - 3)

Factor out 3 (x - 3) from the expression

3 (x - 3) (x - 6 (x - 3))

Solution

3 (x - 3) (- 5 x + 18)

Show Solution

Find the roots

x_{1} = 3, x_{2} = \frac{18}{5}

Alternative Form

x_{1} = 3, x_{2} = 3.6

Evaluate

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

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

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

Multiply the first two terms

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 3

Multiply the terms

6 \times 3

Multiply the numbers

18

18 (x - 3) (x - 3)

Multiply the terms

18 (x - 3)^{2}

3 (x - 3) x - 18 (x - 3)^{2} = 0

Calculate

More Steps

Evaluate

3 (x - 3) x - 18 (x - 3)^{2}

Expand the expression

More Steps

Calculate

3 (x - 3) x

Simplify

(3 x - 9) x

Apply the distributive property

3 x \times x - 9 x

Multiply the terms

3 x^{2} - 9 x

3 x^{2} - 9 x - 18 (x - 3)^{2}

Expand the expression

More Steps

Calculate

- 18 (x - 3)^{2}

Simplify

- 18 (x^{2} - 6 x + 9)

Apply the distributive property

- 18 x^{2} - (- 18 \times 6 x) - 18 \times 9

Multiply the numbers

- 18 x^{2} - (- 108 x) - 18 \times 9

Multiply the numbers

- 18 x^{2} - (- 108 x) - 162

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^{2} + 108 x - 162

3 x^{2} - 9 x - 18 x^{2} + 108 x - 162

Subtract the terms

More Steps

Evaluate

3 x^{2} - 18 x^{2}

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

(3 - 18) x^{2}

Subtract the numbers

- 15 x^{2}

- 15 x^{2} - 9 x + 108 x - 162

Add the terms

More Steps

Evaluate

- 9 x + 108 x

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

(- 9 + 108) x

Add the numbers

99 x

- 15 x^{2} + 99 x - 162

- 15 x^{2} + 99 x - 162 = 0

Factor the expression

More Steps

Evaluate

- 15 x^{2} + 99 x - 162

Rewrite the expression

- 3 \times 5 x^{2} + 3 \times 33 x - 3 \times 54

Factor out - 3 from the expression

- 3 (5 x^{2} - 33 x + 54)

Factor the expression

More Steps

Evaluate

5 x^{2} - 33 x + 54

Rewrite the expression

5 x^{2} + (- 18 - 15) x + 54

Calculate

5 x^{2} - 18 x - 15 x + 54

Rewrite the expression

x \times 5 x - x \times 18 - 3 \times 5 x + 3 \times 18

Factor out x from the expression

x (5 x - 18) - 3 \times 5 x + 3 \times 18

Factor out - 3 from the expression

x (5 x - 18) - 3 (5 x - 18)

Factor out 5 x - 18 from the expression

(x - 3) (5 x - 18)

- 3 (x - 3) (5 x - 18)

- 3 (x - 3) (5 x - 18) = 0

Divide the terms

(x - 3) (5 x - 18) = 0

When the product of factors equals 0,at least one factor is 0

x - 3 = 0 5 x - 18 = 0

Solve the equation for x

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 = 3 5 x - 18 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 18 = 0

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

5 x = 0 + 18

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

5 x = 18

Divide both sides

\frac{5 x}{5} = \frac{18}{5}

Divide the numbers

x = \frac{18}{5}

x = 3 x = \frac{18}{5}

Solution

x_{1} = 3, x_{2} = \frac{18}{5}

Alternative Form

x_{1} = 3, x_{2} = 3.6

Show Solution