10×2-x-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=10⋅-3=-30 and whose sum is b=-1.

Factor -1 out of -x.

10×2-(x)-3=0

Rewrite -1 as 5 plus -6

10×2+(5-6)x-3=0

Apply the distributive property.

10×2+5x-6x-3=0

10×2+5x-6x-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(10×2+5x)-6x-3=0

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

5x(2x+1)-3(2x+1)=0

5x(2x+1)-3(2x+1)=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

(2x+1)(5x-3)=0

(2x+1)(5x-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.

2x+1=0

5x-3=0

Set the first factor equal to 0.

2x+1=0

Subtract 1 from both sides of the equation.

2x=-1

Divide each term by 2 and simplify.

Divide each term in 2x=-1 by 2.

2×2=-12

Cancel the common factor of 2.

Cancel the common factor.

2×2=-12

Divide x by 1.

x=-12

x=-12

Move the negative in front of the fraction.

x=-12

x=-12

x=-12

Set the next factor equal to 0.

5x-3=0

Add 3 to both sides of the equation.

5x=3

Divide each term by 5 and simplify.

Divide each term in 5x=3 by 5.

5×5=35

Cancel the common factor of 5.

Cancel the common factor.

5×5=35

Divide x by 1.

x=35

x=35

x=35

x=35

The final solution is all the values that make (2x+1)(5x-3)=0 true.

x=-12,35

Solve Using the Square Root Property 10x^2-x-3=0