# Solve for s 3s^2+9s-12=0

3s2+9s-12=0
Factor the left side of the equation.
Factor 3 out of 3s2+9s-12.
Factor 3 out of 3s2.
3(s2)+9s-12=0
Factor 3 out of 9s.
3(s2)+3(3s)-12=0
Factor 3 out of -12.
3s2+3(3s)+3⋅-4=0
Factor 3 out of 3s2+3(3s).
3(s2+3s)+3⋅-4=0
Factor 3 out of 3(s2+3s)+3⋅-4.
3(s2+3s-4)=0
3(s2+3s-4)=0
Factor.
Factor s2+3s-4 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 -4 and whose sum is 3.
-1,4
Write the factored form using these integers.
3((s-1)(s+4))=0
3((s-1)(s+4))=0
Remove unnecessary parentheses.
3(s-1)(s+4)=0
3(s-1)(s+4)=0
3(s-1)(s+4)=0
Divide each term by 3 and simplify.
Divide each term in 3(s-1)(s+4)=0 by 3.
3(s-1)(s+4)3=03
Simplify 3(s-1)(s+4)3.
Cancel the common factor of 3.
Cancel the common factor.
3(s-1)(s+4)3=03
Divide (s-1)(s+4) by 1.
(s-1)(s+4)=03
(s-1)(s+4)=03
Expand (s-1)(s+4) using the FOIL Method.
Apply the distributive property.
s(s+4)-1(s+4)=03
Apply the distributive property.
s⋅s+s⋅4-1(s+4)=03
Apply the distributive property.
s⋅s+s⋅4-1s-1⋅4=03
s⋅s+s⋅4-1s-1⋅4=03
Simplify and combine like terms.
Simplify each term.
Multiply s by s.
s2+s⋅4-1s-1⋅4=03
Move 4 to the left of s.
s2+4⋅s-1s-1⋅4=03
Rewrite -1s as -s.
s2+4s-s-1⋅4=03
Multiply -1 by 4.
s2+4s-s-4=03
s2+4s-s-4=03
Subtract s from 4s.
s2+3s-4=03
s2+3s-4=03
s2+3s-4=03
Divide 0 by 3.
s2+3s-4=0
s2+3s-4=0
Factor s2+3s-4 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 -4 and whose sum is 3.
-1,4
Write the factored form using these integers.
(s-1)(s+4)=0
(s-1)(s+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.
s-1=0
s+4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
s-1=0
Add 1 to both sides of the equation.
s=1
s=1
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
s+4=0
Subtract 4 from both sides of the equation.
s=-4
s=-4
The final solution is all the values that make (s-1)(s+4)=0 true.
s=1,-4
Solve for s 3s^2+9s-12=0

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