Trigonometry Examples

$12 d^{2} = - 27 d$

Step 1

Add $27 d$ to both sides of the equation.

$12 d^{2} + 27 d = 0$

Step 2

Factor $3 d$ out of $12 d^{2} + 27 d$ .

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Step 2.1

Factor $3 d$ out of $12 d^{2}$ .

$3 d (4 d) + 27 d = 0$

Step 2.2

Factor $3 d$ out of $27 d$ .

$3 d (4 d) + 3 d (9) = 0$

Step 2.3

Factor $3 d$ out of $3 d (4 d) + 3 d (9)$ .

$3 d (4 d + 9) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$d = 0$

$4 d + 9 = 0$

Step 4

Set $d$ equal to $0$ .

$d = 0$

Step 5

Set $4 d + 9$ equal to $0$ and solve for $d$ .

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Step 5.1

Set $4 d + 9$ equal to $0$ .

$4 d + 9 = 0$

Step 5.2

Solve $4 d + 9 = 0$ for $d$ .

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Step 5.2.1

Subtract $9$ from both sides of the equation.

$4 d = - 9$

Step 5.2.2

Divide each term in $4 d = - 9$ by $4$ and simplify.

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Step 5.2.2.1

Divide each term in $4 d = - 9$ by $4$ .

$\frac{4 d}{4} = \frac{- 9}{4}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{4 d}{4} = \frac{- 9}{4}$

Step 5.2.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{- 9}{4}$

Step 5.2.2.3

Simplify the right side.

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Step 5.2.2.3.1

Move the negative in front of the fraction.

$d = - \frac{9}{4}$

Step 6

The final solution is all the values that make $3 d (4 d + 9) = 0$ true.

$d = 0, - \frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$d = 0, - \frac{9}{4}$

Decimal Form:

$d = 0, - 2.25$

Mixed Number Form:

$d = 0, - 2 \frac{1}{4}$