Precalculus Examples

$7 t^{2} - 8 t = 0$

Step 1

Factor $t$ out of $7 t^{2} - 8 t$ .

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Step 1.1

Factor $t$ out of $7 t^{2}$ .

$t (7 t) - 8 t = 0$

Step 1.2

Factor $t$ out of $- 8 t$ .

$t (7 t) + t \cdot - 8 = 0$

Step 1.3

Factor $t$ out of $t (7 t) + t \cdot - 8$ .

$t (7 t - 8) = 0$

Step 2

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

$t = 0$

$7 t - 8 = 0$

Step 3

Set $t$ equal to $0$ .

$t = 0$

Step 4

Set $7 t - 8$ equal to $0$ and solve for $t$ .

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Step 4.1

Set $7 t - 8$ equal to $0$ .

$7 t - 8 = 0$

Step 4.2

Solve $7 t - 8 = 0$ for $t$ .

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Step 4.2.1

Add $8$ to both sides of the equation.

$7 t = 8$

Step 4.2.2

Divide each term in $7 t = 8$ by $7$ and simplify.

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Step 4.2.2.1

Divide each term in $7 t = 8$ by $7$ .

$\frac{7 t}{7} = \frac{8}{7}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{7 t}{7} = \frac{8}{7}$

Step 4.2.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{8}{7}$

Step 5

The final solution is all the values that make $t (7 t - 8) = 0$ true.

$t = 0, \frac{8}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = 0, \frac{8}{7}$

Decimal Form:

$t = 0, 1.\overline{142857}$

Mixed Number Form:

$t = 0, 1 \frac{1}{7}$