Solve (-5x-4) (-9x^2-6x 7)

Question

Simplify the expression

45 x^{3} + 246 x^{2} + 168 x

Evaluate

(- 5 x - 4) (- 9 x^{2} - 6 x \times 7)

Multiply the terms

(- 5 x - 4) (- 9 x^{2} - 42 x)

Apply the distributive property

- 5 x (- 9 x^{2}) - (- 5 x \times 42 x) - 4 (- 9 x^{2}) - (- 4 \times 42 x)

Multiply the terms

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Evaluate

- 5 x (- 9 x^{2})

Multiply the numbers

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Evaluate

- 5 (- 9)

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

5 \times 9

Multiply the numbers

45

45 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}

45 x^{3}

45 x^{3} - (- 5 x \times 42 x) - 4 (- 9 x^{2}) - (- 4 \times 42 x)

Multiply the terms

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Evaluate

- 5 x \times 42 x

Multiply the numbers

- 210 x \times x

Multiply the terms

- 210 x^{2}

45 x^{3} - (- 210 x^{2}) - 4 (- 9 x^{2}) - (- 4 \times 42 x)

Multiply the numbers

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Evaluate

- 4 (- 9)

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

4 \times 9

Multiply the numbers

36

45 x^{3} - (- 210 x^{2}) + 36 x^{2} - (- 4 \times 42 x)

Multiply the numbers

45 x^{3} - (- 210 x^{2}) + 36 x^{2} - (- 168 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

45 x^{3} + 210 x^{2} + 36 x^{2} + 168 x

Solution

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Evaluate

210 x^{2} + 36 x^{2}

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

(210 + 36) x^{2}

Add the numbers

246 x^{2}

45 x^{3} + 246 x^{2} + 168 x

Show Solution

Factor the expression

3 x (5 x + 4) (3 x + 14)

Evaluate

(- 5 x - 4) (- 9 x^{2} - 6 x \times 7)

Multiply the terms

(- 5 x - 4) (- 9 x^{2} - 42 x)

Factor the expression

- (5 x + 4) (- 9 x^{2} - 42 x)

Factor the expression

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Evaluate

- 9 x^{2} - 42 x

Rewrite the expression

- 3 x \times 3 x - 3 x \times 14

Factor out - 3 x from the expression

- 3 x (3 x + 14)

- (5 x + 4) (- 3 x) (3 x + 14)

Solution

3 x (5 x + 4) (3 x + 14)

Show Solution

Find the roots

x_{1} = - \frac{14}{3}, x_{2} = - \frac{4}{5}, x_{3} = 0

Alternative Form

x_{1} = - 4. \dot{6}, x_{2} = - 0.8, x_{3} = 0

Evaluate

(- 5 x - 4) (- 9 x^{2} - 6 x \times 7)

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

(- 5 x - 4) (- 9 x^{2} - 6 x \times 7) = 0

Multiply the terms

(- 5 x - 4) (- 9 x^{2} - 42 x) = 0

Change the sign

(5 x + 4) (- 9 x^{2} - 42 x) = 0

Separate the equation into 2 possible cases

5 x + 4 = 0 - 9 x^{2} - 42 x = 0

Solve the equation

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Evaluate

5 x + 4 = 0

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

5 x = 0 - 4

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

5 x = - 4

Divide both sides

\frac{5 x}{5} = \frac{- 4}{5}

Divide the numbers

x = \frac{- 4}{5}

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

x = - \frac{4}{5}

x = - \frac{4}{5} - 9 x^{2} - 42 x = 0

Solve the equation

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Evaluate

- 9 x^{2} - 42 x = 0

Factor the expression

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Evaluate

- 9 x^{2} - 42 x

Rewrite the expression

- 3 x \times 3 x - 3 x \times 14

Factor out - 3 x from the expression

- 3 x (3 x + 14)

- 3 x (3 x + 14) = 0

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

- 3 x = 0 3 x + 14 = 0

Solve the equation for x

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Evaluate

- 3 x = 0

Change the signs on both sides of the equation

3 x = 0

Rewrite the expression

x = 0

x = 0 3 x + 14 = 0

Solve the equation for x

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Evaluate

3 x + 14 = 0

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

3 x = 0 - 14

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

3 x = - 14

Divide both sides

\frac{3 x}{3} = \frac{- 14}{3}

Divide the numbers

x = \frac{- 14}{3}

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

x = - \frac{14}{3}

x = 0 x = - \frac{14}{3}

x = - \frac{4}{5} x = 0 x = - \frac{14}{3}

Solution

x_{1} = - \frac{14}{3}, x_{2} = - \frac{4}{5}, x_{3} = 0

Alternative Form

x_{1} = - 4. \dot{6}, x_{2} = - 0.8, x_{3} = 0

Show Solution