# Solve using the Square Root Property 5t^2-2t-3=0 5t2-2t-3=0
Factor by grouping.
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 and solve.
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 and solve.
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

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