Solve (3x-6)^2(x-6)=(3x-6)(x-6)^2

Question

Solve the equation

x_{1} = 0, x_{2} = 2, x_{3} = 6

Evaluate

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

Calculate

More Steps

Calculate

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

Simplify

(9 x^{2} - 36 x + 36) (x - 6)

Apply the distributive property

9 x^{2} \times x - 9 x^{2} \times 6 - 36 x \times x - (- 36 x \times 6) + 36 x - 36 \times 6

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}

9 x^{3} - 9 x^{2} \times 6 - 36 x \times x - (- 36 x \times 6) + 36 x - 36 \times 6

Multiply the numbers

9 x^{3} - 54 x^{2} - 36 x \times x - (- 36 x \times 6) + 36 x - 36 \times 6

Multiply the terms

9 x^{3} - 54 x^{2} - 36 x^{2} - (- 36 x \times 6) + 36 x - 36 \times 6

Multiply the numbers

9 x^{3} - 54 x^{2} - 36 x^{2} - (- 216 x) + 36 x - 36 \times 6

Multiply the numbers

9 x^{3} - 54 x^{2} - 36 x^{2} - (- 216 x) + 36 x - 216

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

9 x^{3} - 54 x^{2} - 36 x^{2} + 216 x + 36 x - 216

Subtract the terms

More Steps

Evaluate

- 54 x^{2} - 36 x^{2}

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

(- 54 - 36) x^{2}

Subtract the numbers

- 90 x^{2}

9 x^{3} - 90 x^{2} + 216 x + 36 x - 216

Add the terms

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Evaluate

216 x + 36 x

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

(216 + 36) x

Add the numbers

252 x

9 x^{3} - 90 x^{2} + 252 x - 216

9 x^{3} - 90 x^{2} + 252 x - 216 = (3 x - 6) (x - 6)^{2}

Calculate

More Steps

Calculate

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

Simplify

(3 x - 6) (x^{2} - 12 x + 36)

Apply the distributive property

3 x \times x^{2} - 3 x \times 12 x + 3 x \times 36 - 6 x^{2} - (- 6 \times 12 x) - 6 \times 36

Multiply the terms

More Steps

Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

3 x^{3} - 3 x \times 12 x + 3 x \times 36 - 6 x^{2} - (- 6 \times 12 x) - 6 \times 36

Multiply the terms

More Steps

Evaluate

3 x \times 12 x

Multiply the numbers

36 x \times x

Multiply the terms

36 x^{2}

3 x^{3} - 36 x^{2} + 3 x \times 36 - 6 x^{2} - (- 6 \times 12 x) - 6 \times 36

Multiply the numbers

3 x^{3} - 36 x^{2} + 108 x - 6 x^{2} - (- 6 \times 12 x) - 6 \times 36

Multiply the numbers

3 x^{3} - 36 x^{2} + 108 x - 6 x^{2} - (- 72 x) - 6 \times 36

Multiply the numbers

3 x^{3} - 36 x^{2} + 108 x - 6 x^{2} - (- 72 x) - 216

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 x^{3} - 36 x^{2} + 108 x - 6 x^{2} + 72 x - 216

Subtract the terms

More Steps

Evaluate

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

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

(- 36 - 6) x^{2}

Subtract the numbers

- 42 x^{2}

3 x^{3} - 42 x^{2} + 108 x + 72 x - 216

Add the terms

More Steps

Evaluate

108 x + 72 x

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

(108 + 72) x

Add the numbers

180 x

3 x^{3} - 42 x^{2} + 180 x - 216

9 x^{3} - 90 x^{2} + 252 x - 216 = 3 x^{3} - 42 x^{2} + 180 x - 216

Move the expression to the left side

9 x^{3} - 90 x^{2} + 252 x - 216 - (3 x^{3} - 42 x^{2} + 180 x - 216) = 0

Calculate the sum or difference

More Steps

Add the terms

9 x^{3} - 90 x^{2} + 252 x - 216 - (3 x^{3} - 42 x^{2} + 180 x - 216)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

9 x^{3} - 90 x^{2} + 252 x - 216 - 3 x^{3} + 42 x^{2} - 180 x + 216

Subtract the terms

More Steps

Evaluate

9 x^{3} - 3 x^{3}

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

(9 - 3) x^{3}

Subtract the numbers

6 x^{3}

6 x^{3} - 90 x^{2} + 252 x - 216 + 42 x^{2} - 180 x + 216

Add the terms

More Steps

Evaluate

- 90 x^{2} + 42 x^{2}

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

(- 90 + 42) x^{2}

Add the numbers

- 48 x^{2}

6 x^{3} - 48 x^{2} + 252 x - 216 - 180 x + 216

Subtract the terms

More Steps

Evaluate

252 x - 180 x

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

(252 - 180) x

Subtract the numbers

72 x

6 x^{3} - 48 x^{2} + 72 x - 216 + 216

Since two opposites add up to 0,remove them form the expression

6 x^{3} - 48 x^{2} + 72 x

6 x^{3} - 48 x^{2} + 72 x = 0

Factor the expression

6 x (x - 6) (x - 2) = 0

Divide both sides

x (x - 6) (x - 2) = 0

Separate the equation into 3 possible cases

x = 0 x - 6 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 0 x = 6 x - 2 = 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 = 6 x = 2

Solution

x_{1} = 0, x_{2} = 2, x_{3} = 6

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Solve the equation

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