# Solve for t 5t^2+10t-40=0 5t2+10t-40=0
Factor the left side of the equation.
Factor 5 out of 5t2+10t-40.
Factor 5 out of 5t2.
5(t2)+10t-40=0
Factor 5 out of 10t.
5(t2)+5(2t)-40=0
Factor 5 out of -40.
5t2+5(2t)+5⋅-8=0
Factor 5 out of 5t2+5(2t).
5(t2+2t)+5⋅-8=0
Factor 5 out of 5(t2+2t)+5⋅-8.
5(t2+2t-8)=0
5(t2+2t-8)=0
Factor.
Factor t2+2t-8 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 -8 and whose sum is 2.
-2,4
Write the factored form using these integers.
5((t-2)(t+4))=0
5((t-2)(t+4))=0
Remove unnecessary parentheses.
5(t-2)(t+4)=0
5(t-2)(t+4)=0
5(t-2)(t+4)=0
Divide each term by 5 and simplify.
Divide each term in 5(t-2)(t+4)=0 by 5.
5(t-2)(t+4)5=05
Simplify 5(t-2)(t+4)5.
Cancel the common factor of 5.
Cancel the common factor.
5(t-2)(t+4)5=05
Divide (t-2)(t+4) by 1.
(t-2)(t+4)=05
(t-2)(t+4)=05
Expand (t-2)(t+4) using the FOIL Method.
Apply the distributive property.
t(t+4)-2(t+4)=05
Apply the distributive property.
t⋅t+t⋅4-2(t+4)=05
Apply the distributive property.
t⋅t+t⋅4-2t-2⋅4=05
t⋅t+t⋅4-2t-2⋅4=05
Simplify and combine like terms.
Simplify each term.
Multiply t by t.
t2+t⋅4-2t-2⋅4=05
Move 4 to the left of t.
t2+4⋅t-2t-2⋅4=05
Multiply -2 by 4.
t2+4t-2t-8=05
t2+4t-2t-8=05
Subtract 2t from 4t.
t2+2t-8=05
t2+2t-8=05
t2+2t-8=05
Divide 0 by 5.
t2+2t-8=0
t2+2t-8=0
Factor t2+2t-8 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 -8 and whose sum is 2.
-2,4
Write the factored form using these integers.
(t-2)(t+4)=0
(t-2)(t+4)=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-2=0
t+4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
t-2=0
Add 2 to both sides of the equation.
t=2
t=2
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
t+4=0
Subtract 4 from both sides of the equation.
t=-4
t=-4
The final solution is all the values that make (t-2)(t+4)=0 true.
t=2,-4
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