5s2-11s=12

Move 12 to the left side of the equation by subtracting it from both sides.

5s2-11s-12=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅-12=-60 and whose sum is b=-11.

Factor -11 out of -11s.

5s2-11s-12=0

Rewrite -11 as 4 plus -15

5s2+(4-15)s-12=0

Apply the distributive property.

5s2+4s-15s-12=0

5s2+4s-15s-12=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5s2+4s)-15s-12=0

Factor out the greatest common factor (GCF) from each group.

s(5s+4)-3(5s+4)=0

s(5s+4)-3(5s+4)=0

Factor the polynomial by factoring out the greatest common factor, 5s+4.

(5s+4)(s-3)=0

(5s+4)(s-3)=0

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

5s+4=0

s-3=0

Set the first factor equal to 0.

5s+4=0

Subtract 4 from both sides of the equation.

5s=-4

Divide each term by 5 and simplify.

Divide each term in 5s=-4 by 5.

5s5=-45

Cancel the common factor of 5.

Cancel the common factor.

5s5=-45

Divide s by 1.

s=-45

s=-45

Move the negative in front of the fraction.

s=-45

s=-45

s=-45

Set the next factor equal to 0.

s-3=0

Add 3 to both sides of the equation.

s=3

s=3

The final solution is all the values that make (5s+4)(s-3)=0 true.

s=-45,3

The result can be shown in multiple forms.

Exact Form:

s=-45,3

Decimal Form:

s=-0.8,3

Solve for s 5s^2-11s=12