6×2-11x-21=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=6⋅-21=-126 and whose sum is b=-11.

Factor -11 out of -11x.

6×2-11x-21=0

Rewrite -11 as 7 plus -18

6×2+(7-18)x-21=0

Apply the distributive property.

6×2+7x-18x-21=0

6×2+7x-18x-21=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6×2+7x)-18x-21=0

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

x(6x+7)-3(6x+7)=0

x(6x+7)-3(6x+7)=0

Factor the polynomial by factoring out the greatest common factor, 6x+7.

(6x+7)(x-3)=0

(6x+7)(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.

6x+7=0

x-3=0

Set the first factor equal to 0.

6x+7=0

Subtract 7 from both sides of the equation.

6x=-7

Divide each term by 6 and simplify.

Divide each term in 6x=-7 by 6.

6×6=-76

Cancel the common factor of 6.

Cancel the common factor.

6×6=-76

Divide x by 1.

x=-76

x=-76

Move the negative in front of the fraction.

x=-76

x=-76

x=-76

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 (6x+7)(x-3)=0 true.

x=-76,3

Solve Using the Square Root Property 6x^2-11x-21=0