Solve (4d-6) (-9d-7)

Question

Simplify the expression

- 36 d^{2} + 26 d + 42

Evaluate

(4 d - 6) (- 9 d - 7)

Apply the distributive property

4 d (- 9 d) - 4 d \times 7 - 6 (- 9 d) - (- 6 \times 7)

Multiply the terms

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Evaluate

4 d (- 9 d)

Multiply the numbers

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Evaluate

4 (- 9)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 9

Multiply the numbers

- 36

- 36 d \times d

Multiply the terms

- 36 d^{2}

- 36 d^{2} - 4 d \times 7 - 6 (- 9 d) - (- 6 \times 7)

Multiply the numbers

- 36 d^{2} - 28 d - 6 (- 9 d) - (- 6 \times 7)

Multiply the numbers

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Evaluate

- 6 (- 9)

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

6 \times 9

Multiply the numbers

54

- 36 d^{2} - 28 d + 54 d - (- 6 \times 7)

Multiply the numbers

- 36 d^{2} - 28 d + 54 d - (- 42)

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

- 36 d^{2} - 28 d + 54 d + 42

Solution

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Evaluate

- 28 d + 54 d

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

(- 28 + 54) d

Add the numbers

26 d

- 36 d^{2} + 26 d + 42

Show Solution

Factor the expression

- 2 (2 d - 3) (9 d + 7)

Evaluate

(4 d - 6) (- 9 d - 7)

Factor the expression

2 (2 d - 3) (- 9 d - 7)

Factor the expression

2 (2 d - 3) (- 1) (9 d + 7)

Solution

- 2 (2 d - 3) (9 d + 7)

Show Solution

Find the roots

d_{1} = - \frac{7}{9}, d_{2} = \frac{3}{2}

Alternative Form

d_{1} = - 0. \dot{7}, d_{2} = 1.5

Evaluate

(4 d - 6) (- 9 d - 7)

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

(4 d - 6) (- 9 d - 7) = 0

Separate the equation into 2 possible cases

4 d - 6 = 0 - 9 d - 7 = 0

Solve the equation

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Evaluate

4 d - 6 = 0

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

4 d = 0 + 6

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

4 d = 6

Divide both sides

\frac{4 d}{4} = \frac{6}{4}

Divide the numbers

d = \frac{6}{4}

Cancel out the common factor 2

d = \frac{3}{2}

d = \frac{3}{2} - 9 d - 7 = 0

Solve the equation

More Steps

Evaluate

- 9 d - 7 = 0

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

- 9 d = 0 + 7

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

- 9 d = 7

Change the signs on both sides of the equation

9 d = - 7

Divide both sides

\frac{9 d}{9} = \frac{- 7}{9}

Divide the numbers

d = \frac{- 7}{9}

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

d = - \frac{7}{9}

d = \frac{3}{2} d = - \frac{7}{9}

Solution

d_{1} = - \frac{7}{9}, d_{2} = \frac{3}{2}

Alternative Form

d_{1} = - 0. \dot{7}, d_{2} = 1.5

Show Solution