Solve (6x-54x^(2)) (2x-2)

Question

Simplify the expression

120 x^{2} - 12 x - 108 x^{3}

Evaluate

(6 x - 54 x^{2}) (2 x - 2)

Apply the distributive property

6 x \times 2 x - 6 x \times 2 - 54 x^{2} \times 2 x - (- 54 x^{2} \times 2)

Multiply the terms

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Evaluate

6 x \times 2 x

Multiply the numbers

12 x \times x

Multiply the terms

12 x^{2}

12 x^{2} - 6 x \times 2 - 54 x^{2} \times 2 x - (- 54 x^{2} \times 2)

Multiply the numbers

12 x^{2} - 12 x - 54 x^{2} \times 2 x - (- 54 x^{2} \times 2)

Multiply the terms

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Evaluate

- 54 x^{2} \times 2 x

Multiply the numbers

- 108 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}

- 108 x^{3}

12 x^{2} - 12 x - 108 x^{3} - (- 54 x^{2} \times 2)

Multiply the numbers

12 x^{2} - 12 x - 108 x^{3} - (- 108 x^{2})

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

12 x^{2} - 12 x - 108 x^{3} + 108 x^{2}

Solution

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Evaluate

12 x^{2} + 108 x^{2}

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

(12 + 108) x^{2}

Add the numbers

120 x^{2}

120 x^{2} - 12 x - 108 x^{3}

Show Solution

Factor the expression

12 x (1 - 9 x) (x - 1)

Evaluate

(6 x - 54 x^{2}) (2 x - 2)

Factor the expression

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Evaluate

6 x - 54 x^{2}

Rewrite the expression

6 x - 6 x \times 9 x

Factor out 6 x from the expression

6 x (1 - 9 x)

6 x (1 - 9 x) (2 x - 2)

Factor the expression

6 x (1 - 9 x) \times 2 (x - 1)

Solution

12 x (1 - 9 x) (x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{9}, x_{3} = 1

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{1}, x_{3} = 1

Evaluate

(6 x - 54 x^{2}) (2 x - 2)

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

(6 x - 54 x^{2}) (2 x - 2) = 0

Separate the equation into 2 possible cases

6 x - 54 x^{2} = 0 2 x - 2 = 0

Solve the equation

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Evaluate

6 x - 54 x^{2} = 0

Factor the expression

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Evaluate

6 x - 54 x^{2}

Rewrite the expression

6 x - 6 x \times 9 x

Factor out 6 x from the expression

6 x (1 - 9 x)

6 x (1 - 9 x) = 0

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

6 x = 0 1 - 9 x = 0

Solve the equation for x

x = 0 1 - 9 x = 0

Solve the equation for x

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Evaluate

1 - 9 x = 0

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

- 9 x = 0 - 1

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

- 9 x = - 1

Change the signs on both sides of the equation

9 x = 1

Divide both sides

\frac{9 x}{9} = \frac{1}{9}

Divide the numbers

x = \frac{1}{9}

x = 0 x = \frac{1}{9}

x = 0 x = \frac{1}{9} 2 x - 2 = 0

Solve the equation

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Evaluate

2 x - 2 = 0

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

2 x = 0 + 2

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

2 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{2}

Divide the numbers

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Evaluate

\frac{2}{2}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 0 x = \frac{1}{9} x = 1

Solution

x_{1} = 0, x_{2} = \frac{1}{9}, x_{3} = 1

Alternative Form

x_{1} = 0, x_{2} = 0. \dot{1}, x_{3} = 1

Show Solution