0=-16t2+66.4t

Rewrite the equation as -16t2+66.4t=0.

-16t2+66.4t=0

Factor -0.8t out of -16t2.

-0.8t(20t)+66.4t=0

Factor -0.8t out of 66.4t.

-0.8t(20t)-0.8t⋅-83=0

Factor -0.8t out of -0.8t(20t)-0.8t(-83).

-0.8t(20t-83)=0

-0.8t(20t-83)=0

Divide each term in -0.8t(20t-83)=0 by -0.8.

-0.8t(20t-83)-0.8=0-0.8

Cancel the common factor of -0.8.

20t2-83t=0-0.8

Divide 0 by -0.8.

20t2-83t=0

20t2-83t=0

Factor t out of 20t2.

t(20t)-83t=0

Factor t out of -83t.

t(20t)+t⋅-83=0

Factor t out of t(20t)+t⋅-83.

t(20t-83)=0

t(20t-83)=0

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

20t-83=0

Set the first factor equal to 0.

t=0

Set the next factor equal to 0.

20t-83=0

Add 83 to both sides of the equation.

20t=83

Divide each term by 20 and simplify.

Divide each term in 20t=83 by 20.

20t20=8320

Cancel the common factor of 20.

Cancel the common factor.

20t20=8320

Divide t by 1.

t=8320

t=8320

t=8320

t=8320

The final solution is all the values that make t(20t-83)=0 true.

t=0,8320

Solve Using the Square Root Property 0=-16t^2+66.4t