Trigonometry Examples

$462 (t) = 13 t^{2} - 73 t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$13 t^{2} - 73 t = 462 t$

Step 2

Move all terms containing $t$ to the left side of the equation.

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Step 2.1

Subtract $462 t$ from both sides of the equation.

$13 t^{2} - 73 t - 462 t = 0$

Step 2.2

Subtract $462 t$ from $- 73 t$ .

$13 t^{2} - 535 t = 0$

Step 3

Factor $t$ out of $13 t^{2} - 535 t$ .

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Step 3.1

Factor $t$ out of $13 t^{2}$ .

$t (13 t) - 535 t = 0$

Step 3.2

Factor $t$ out of $- 535 t$ .

$t (13 t) + t \cdot - 535 = 0$

Step 3.3

Factor $t$ out of $t (13 t) + t \cdot - 535$ .

$t (13 t - 535) = 0$

Step 4

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

$t = 0$

$13 t - 535 = 0$

Step 5

Set $t$ equal to $0$ .

$t = 0$

Step 6

Set $13 t - 535$ equal to $0$ and solve for $t$ .

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Step 6.1

Set $13 t - 535$ equal to $0$ .

$13 t - 535 = 0$

Step 6.2

Solve $13 t - 535 = 0$ for $t$ .

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Step 6.2.1

Add $535$ to both sides of the equation.

$13 t = 535$

Step 6.2.2

Divide each term in $13 t = 535$ by $13$ and simplify.

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Step 6.2.2.1

Divide each term in $13 t = 535$ by $13$ .

$\frac{13 t}{13} = \frac{535}{13}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $13$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{13 t}{13} = \frac{535}{13}$

Step 6.2.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{535}{13}$

Step 7

The final solution is all the values that make $t (13 t - 535) = 0$ true.

$t = 0, \frac{535}{13}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$t = 0, \frac{535}{13}$

Decimal Form:

$t = 0, 41.15384615 \dots$

Mixed Number Form:

$t = 0, 41 \frac{2}{13}$