# Solve for t 0=-16t^2+32t+768

0=-16t2+32t+768
Rewrite the equation as -16t2+32t+768=0.
-16t2+32t+768=0
Factor the left side of the equation.
Factor -16 out of -16t2+32t+768.
Factor -16 out of -16t2.
-16t2+32t+768=0
Factor -16 out of 32t.
-16t2-16(-2t)+768=0
Factor -16 out of 768.
-16t2-16(-2t)-16⋅-48=0
Factor -16 out of -16(t2)-16(-2t).
-16(t2-2t)-16⋅-48=0
Factor -16 out of -16(t2-2t)-16(-48).
-16(t2-2t-48)=0
-16(t2-2t-48)=0
Factor.
Factor t2-2t-48 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -48 and whose sum is -2.
-8,6
Write the factored form using these integers.
-16((t-8)(t+6))=0
-16((t-8)(t+6))=0
Remove unnecessary parentheses.
-16(t-8)(t+6)=0
-16(t-8)(t+6)=0
-16(t-8)(t+6)=0
Divide each term by -16 and simplify.
Divide each term in -16(t-8)(t+6)=0 by -16.
-16(t-8)(t+6)-16=0-16
Simplify -16(t-8)(t+6)-16.
Cancel the common factor of -16.
Cancel the common factor.
-16(t-8)(t+6)-16=0-16
Divide (t-8)(t+6) by 1.
(t-8)(t+6)=0-16
(t-8)(t+6)=0-16
Expand (t-8)(t+6) using the FOIL Method.
Apply the distributive property.
t(t+6)-8(t+6)=0-16
Apply the distributive property.
t⋅t+t⋅6-8(t+6)=0-16
Apply the distributive property.
t⋅t+t⋅6-8t-8⋅6=0-16
t⋅t+t⋅6-8t-8⋅6=0-16
Simplify and combine like terms.
Simplify each term.
Multiply t by t.
t2+t⋅6-8t-8⋅6=0-16
Move 6 to the left of t.
t2+6⋅t-8t-8⋅6=0-16
Multiply -8 by 6.
t2+6t-8t-48=0-16
t2+6t-8t-48=0-16
Subtract 8t from 6t.
t2-2t-48=0-16
t2-2t-48=0-16
t2-2t-48=0-16
Divide 0 by -16.
t2-2t-48=0
t2-2t-48=0
Factor t2-2t-48 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -48 and whose sum is -2.
-8,6
Write the factored form using these integers.
(t-8)(t+6)=0
(t-8)(t+6)=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-8=0
t+6=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
t-8=0
Add 8 to both sides of the equation.
t=8
t=8
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
t+6=0
Subtract 6 from both sides of the equation.
t=-6
t=-6
The final solution is all the values that make (t-8)(t+6)=0 true.
t=8,-6
Solve for t 0=-16t^2+32t+768

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