Solve 27 d-2(-3d^27 )

Question

Simplify the expression

27 d + 42 d^{2}

Evaluate

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

Rewrite the expression

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

Multiply

More Steps

Multiply the terms

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

Rewrite the expression

- 2 \times 3 d^{2} \times 7

Multiply the terms

More Steps

Evaluate

2 \times 3 \times 7

Multiply the terms

6 \times 7

Multiply the numbers

42

- 42 d^{2}

27 d - (- 42 d^{2})

Solution

27 d + 42 d^{2}

Show Solution

Factor the expression

3 d (9 + 14 d)

Evaluate

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

Multiply the terms

27 d - 2 (- 21 d^{2})

Multiply the numbers

More Steps

Evaluate

2 (- 21)

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

- 2 \times 21

Multiply the numbers

- 42

Evaluate

- 42 d^{2}

27 d - (- 42 d^{2})

Rewrite the expression

27 d + 42 d^{2}

Rewrite the expression

3 d \times 9 + 3 d \times 14 d

Solution

3 d (9 + 14 d)

Show Solution

Find the roots

d_{1} = - \frac{9}{14}, d_{2} = 0

Alternative Form

d_{1} = - 0.6 \dot{4} 2857 \dot{1}, d_{2} = 0

Evaluate

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

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

27 d - 2 (- 3 d^{2} \times 7) = 0

Multiply the terms

27 d - 2 (- 21 d^{2}) = 0

Multiply the numbers

More Steps

Evaluate

2 (- 21)

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

- 2 \times 21

Multiply the numbers

- 42

27 d - (- 42 d^{2}) = 0

Rewrite the expression

27 d + 42 d^{2} = 0

Factor the expression

More Steps

Evaluate

27 d + 42 d^{2}

Rewrite the expression

3 d \times 9 + 3 d \times 14 d

Factor out 3 d from the expression

3 d (9 + 14 d)

3 d (9 + 14 d) = 0

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

3 d = 0 9 + 14 d = 0

Solve the equation for d

d = 0 9 + 14 d = 0

Solve the equation for d

More Steps

Evaluate

9 + 14 d = 0

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

14 d = 0 - 9

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

14 d = - 9

Divide both sides

\frac{14 d}{14} = \frac{- 9}{14}

Divide the numbers

d = \frac{- 9}{14}

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

d = - \frac{9}{14}

d = 0 d = - \frac{9}{14}

Solution

d_{1} = - \frac{9}{14}, d_{2} = 0

Alternative Form

d_{1} = - 0.6 \dot{4} 2857 \dot{1}, d_{2} = 0

Show Solution