7×2+2x-5=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=7⋅-5=-35 and whose sum is b=2.

Factor 2 out of 2x.

7×2+2(x)-5=0

Rewrite 2 as -5 plus 7

7×2+(-5+7)x-5=0

Apply the distributive property.

7×2-5x+7x-5=0

7×2-5x+7x-5=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(7×2-5x)+7x-5=0

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

x(7x-5)+1(7x-5)=0

x(7x-5)+1(7x-5)=0

Factor the polynomial by factoring out the greatest common factor, 7x-5.

(7x-5)(x+1)=0

(7x-5)(x+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.

7x-5=0

x+1=0

Set the first factor equal to 0.

7x-5=0

Add 5 to both sides of the equation.

7x=5

Divide each term by 7 and simplify.

Divide each term in 7x=5 by 7.

7×7=57

Cancel the common factor of 7.

Cancel the common factor.

7×7=57

Divide x by 1.

x=57

x=57

x=57

x=57

Set the next factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

The final solution is all the values that make (7x-5)(x+1)=0 true.

x=57,-1

Solve using the Square Root Property 7x^2+2x-5=0