5t2-2t-3=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⋅-3=-15 and whose sum is b=-2.

Factor -2 out of -2t.

5t2-2t-3=0

Rewrite -2 as 3 plus -5

5t2+(3-5)t-3=0

Apply the distributive property.

5t2+3t-5t-3=0

5t2+3t-5t-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5t2+3t)-5t-3=0

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

t(5t+3)-(5t+3)=0

t(5t+3)-(5t+3)=0

Factor the polynomial by factoring out the greatest common factor, 5t+3.

(5t+3)(t-1)=0

(5t+3)(t-1)=0

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

5t+3=0

t-1=0

Set the first factor equal to 0.

5t+3=0

Subtract 3 from both sides of the equation.

5t=-3

Divide each term by 5 and simplify.

Divide each term in 5t=-3 by 5.

5t5=-35

Cancel the common factor of 5.

Cancel the common factor.

5t5=-35

Divide t by 1.

t=-35

t=-35

Move the negative in front of the fraction.

t=-35

t=-35

t=-35

Set the next factor equal to 0.

t-1=0

Add 1 to both sides of the equation.

t=1

t=1

The final solution is all the values that make (5t+3)(t-1)=0 true.

t=-35,1

Solve using the Square Root Property 5t^2-2t-3=0