# Solve Using the Square Root Property 6x^2-7x-3=0

6×2-7x-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=6⋅-3=-18 and whose sum is b=-7.
Factor -7 out of -7x.
6×2-7x-3=0
Rewrite -7 as 2 plus -9
6×2+(2-9)x-3=0
Apply the distributive property.
6×2+2x-9x-3=0
6×2+2x-9x-3=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(6×2+2x)-9x-3=0
Factor out the greatest common factor (GCF) from each group.
2x(3x+1)-3(3x+1)=0
2x(3x+1)-3(3x+1)=0
Factor the polynomial by factoring out the greatest common factor, 3x+1.
(3x+1)(2x-3)=0
(3x+1)(2x-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.
3x+1=0
2x-3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3x+1=0
Subtract 1 from both sides of the equation.
3x=-1
Divide each term by 3 and simplify.
Divide each term in 3x=-1 by 3.
3×3=-13
Cancel the common factor of 3.
Cancel the common factor.
3×3=-13
Divide x by 1.
x=-13
x=-13
Move the negative in front of the fraction.
x=-13
x=-13
x=-13
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
2x-3=0
Add 3 to both sides of the equation.
2x=3
Divide each term by 2 and simplify.
Divide each term in 2x=3 by 2.
2×2=32
Cancel the common factor of 2.
Cancel the common factor.
2×2=32
Divide x by 1.
x=32
x=32
x=32
x=32
The final solution is all the values that make (3x+1)(2x-3)=0 true.
x=-13,32
Solve Using the Square Root Property 6x^2-7x-3=0