Solve (-3d - 7) (-3d - 1)

Question

Simplify the expression

9 d^{2} + 24 d + 7

Evaluate

(- 3 d - 7) (- 3 d - 1)

Apply the distributive property

- 3 d (- 3 d) - (- 3 d \times 1) - 7 (- 3 d) - (- 7 \times 1)

Multiply the terms

More Steps

Evaluate

- 3 d (- 3 d)

Multiply the numbers

More Steps

Evaluate

- 3 (- 3)

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

3 \times 3

Multiply the numbers

9

9 d \times d

Multiply the terms

9 d^{2}

9 d^{2} - (- 3 d \times 1) - 7 (- 3 d) - (- 7 \times 1)

Any expression multiplied by 1 remains the same

9 d^{2} - (- 3 d) - 7 (- 3 d) - (- 7 \times 1)

Multiply the numbers

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Evaluate

- 7 (- 3)

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

7 \times 3

Multiply the numbers

21

9 d^{2} - (- 3 d) + 21 d - (- 7 \times 1)

Any expression multiplied by 1 remains the same

9 d^{2} - (- 3 d) + 21 d - (- 7)

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 d^{2} + 3 d + 21 d + 7

Solution

More Steps

Evaluate

3 d + 21 d

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

(3 + 21) d

Add the numbers

24 d

9 d^{2} + 24 d + 7

Show Solution

Find the roots

d_{1} = - \frac{7}{3}, d_{2} = - \frac{1}{3}

Alternative Form

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

Evaluate

(- 3 d - 7) (- 3 d - 1)

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

(- 3 d - 7) (- 3 d - 1) = 0

Change the sign

(3 d + 7) (- 3 d - 1) = 0

Separate the equation into 2 possible cases

3 d + 7 = 0 - 3 d - 1 = 0

Solve the equation

More Steps

Evaluate

3 d + 7 = 0

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

3 d = 0 - 7

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

3 d = - 7

Divide both sides

\frac{3 d}{3} = \frac{- 7}{3}

Divide the numbers

d = \frac{- 7}{3}

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

d = - \frac{7}{3}

d = - \frac{7}{3} - 3 d - 1 = 0

Solve the equation

More Steps

Evaluate

- 3 d - 1 = 0

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

- 3 d = 0 + 1

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

- 3 d = 1

Change the signs on both sides of the equation

3 d = - 1

Divide both sides

\frac{3 d}{3} = \frac{- 1}{3}

Divide the numbers

d = \frac{- 1}{3}

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

d = - \frac{1}{3}

d = - \frac{7}{3} d = - \frac{1}{3}

Solution

d_{1} = - \frac{7}{3}, d_{2} = - \frac{1}{3}

Alternative Form

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

Show Solution