Solve (x-6)⋅(-3x^(2)-5x-2)

Question

Simplify the expression

- 3 x^{3} + 13 x^{2} + 28 x + 12

Evaluate

(x - 6) (- 3 x^{2} - 5 x - 2)

Apply the distributive property

x (- 3 x^{2}) - x \times 5 x - x \times 2 - 6 (- 3 x^{2}) - (- 6 \times 5 x) - (- 6 \times 2)

Multiply the terms

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Evaluate

x (- 3 x^{2})

Use the commutative property to reorder the terms

- 3 x \times x^{2}

Multiply the terms

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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^{3} - x \times 5 x - x \times 2 - 6 (- 3 x^{2}) - (- 6 \times 5 x) - (- 6 \times 2)

Multiply the terms

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Evaluate

x \times 5 x

Use the commutative property to reorder the terms

5 x \times x

Multiply the terms

5 x^{2}

- 3 x^{3} - 5 x^{2} - x \times 2 - 6 (- 3 x^{2}) - (- 6 \times 5 x) - (- 6 \times 2)

Use the commutative property to reorder the terms

- 3 x^{3} - 5 x^{2} - 2 x - 6 (- 3 x^{2}) - (- 6 \times 5 x) - (- 6 \times 2)

Multiply the numbers

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Evaluate

- 6 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

6 \times 3

Multiply the numbers

18

- 3 x^{3} - 5 x^{2} - 2 x + 18 x^{2} - (- 6 \times 5 x) - (- 6 \times 2)

Multiply the numbers

- 3 x^{3} - 5 x^{2} - 2 x + 18 x^{2} - (- 30 x) - (- 6 \times 2)

Multiply the numbers

- 3 x^{3} - 5 x^{2} - 2 x + 18 x^{2} - (- 30 x) - (- 12)

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} - 5 x^{2} - 2 x + 18 x^{2} + 30 x + 12

Add the terms

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Evaluate

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

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

(- 5 + 18) x^{2}

Add the numbers

13 x^{2}

- 3 x^{3} + 13 x^{2} - 2 x + 30 x + 12

Solution

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Evaluate

- 2 x + 30 x

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

(- 2 + 30) x

Add the numbers

28 x

- 3 x^{3} + 13 x^{2} + 28 x + 12

Show Solution

Factor the expression

- (x - 6) (x + 1) (3 x + 2)

Evaluate

(x - 6) (- 3 x^{2} - 5 x - 2)

Factor the expression

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Evaluate

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

Factor out - 1 from the expression

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

Factor the expression

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Evaluate

3 x^{2} + 5 x + 2

Rewrite the expression

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

Calculate

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

Rewrite the expression

x \times 3 x + x \times 2 + 3 x + 2

Factor out x from the expression

x (3 x + 2) + 3 x + 2

Factor out 3 x + 2 from the expression

(x + 1) (3 x + 2)

- (x + 1) (3 x + 2)

(x - 6) (- 1) (x + 1) (3 x + 2)

Solution

- (x - 6) (x + 1) (3 x + 2)

Show Solution

Find the roots

x_{1} = - 1, x_{2} = - \frac{2}{3}, x_{3} = 6

Alternative Form

x_{1} = - 1, x_{2} = - 0. \dot{6}, x_{3} = 6

Evaluate

(x - 6) (- 3 x^{2} - 5 x - 2)

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

(x - 6) (- 3 x^{2} - 5 x - 2) = 0

Separate the equation into 2 possible cases

x - 6 = 0 - 3 x^{2} - 5 x - 2 = 0

Solve the equation

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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 = 6 - 3 x^{2} - 5 x - 2 = 0

Solve the equation

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Evaluate

- 3 x^{2} - 5 x - 2 = 0

Factor the expression

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Evaluate

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

Factor out - 1 from the expression

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

Factor the expression

- (x + 1) (3 x + 2)

- (x + 1) (3 x + 2) = 0

Divide the terms

(x + 1) (3 x + 2) = 0

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

x + 1 = 0 3 x + 2 = 0

Solve the equation for x

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Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = - 1 3 x + 2 = 0

Solve the equation for x

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Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{2}{3}

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

x = 6 x = - 1 x = - \frac{2}{3}

Solution

x_{1} = - 1, x_{2} = - \frac{2}{3}, x_{3} = 6

Alternative Form

x_{1} = - 1, x_{2} = - 0. \dot{6}, x_{3} = 6

Show Solution