Precalculus Examples

$- 16 t^{2} + 160 t = 0$

Step 1

Factor $- 16 t$ out of $- 16 t^{2} + 160 t$ .

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Step 1.1

Factor $- 16 t$ out of $- 16 t^{2}$ .

$- 16 t \cdot t + 160 t = 0$

Step 1.2

Factor $- 16 t$ out of $160 t$ .

$- 16 t \cdot t - 16 t \cdot - 10 = 0$

Step 1.3

Factor $- 16 t$ out of $- 16 t (t) - 16 t (- 10)$ .

$- 16 t (t - 10) = 0$

Step 2

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

$t = 0$

$t - 10 = 0$

Step 3

Set $t$ equal to $0$ .

$t = 0$

Step 4

Set $t - 10$ equal to $0$ and solve for $t$ .

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Step 4.1

Set $t - 10$ equal to $0$ .

$t - 10 = 0$

Step 4.2

Add $10$ to both sides of the equation.

$t = 10$

Step 5

The final solution is all the values that make $- 16 t (t - 10) = 0$ true.

$t = 0, 10$