7×2-12x-27=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⋅-27=-189 and whose sum is b=-12.

Factor -12 out of -12x.

7×2-12x-27=0

Rewrite -12 as 9 plus -21

7×2+(9-21)x-27=0

Apply the distributive property.

7×2+9x-21x-27=0

7×2+9x-21x-27=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(7×2+9x)-21x-27=0

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

x(7x+9)-3(7x+9)=0

x(7x+9)-3(7x+9)=0

Factor the polynomial by factoring out the greatest common factor, 7x+9.

(7x+9)(x-3)=0

(7x+9)(x-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.

7x+9=0

x-3=0

Set the first factor equal to 0.

7x+9=0

Subtract 9 from both sides of the equation.

7x=-9

Divide each term by 7 and simplify.

Divide each term in 7x=-9 by 7.

7×7=-97

Cancel the common factor of 7.

Cancel the common factor.

7×7=-97

Divide x by 1.

x=-97

x=-97

Move the negative in front of the fraction.

x=-97

x=-97

x=-97

Set the next factor equal to 0.

x-3=0

Add 3 to both sides of the equation.

x=3

x=3

The final solution is all the values that make (7x+9)(x-3)=0 true.

x=-97,3

Solve using the Square Root Property 7x^2-12x-27=0