3×2-20x-32=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=3⋅-32=-96 and whose sum is b=-20.

Factor -20 out of -20x.

3×2-20x-32=0

Rewrite -20 as 4 plus -24

3×2+(4-24)x-32=0

Apply the distributive property.

3×2+4x-24x-32=0

3×2+4x-24x-32=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2+4x)-24x-32=0

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

x(3x+4)-8(3x+4)=0

x(3x+4)-8(3x+4)=0

Factor the polynomial by factoring out the greatest common factor, 3x+4.

(3x+4)(x-8)=0

(3x+4)(x-8)=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+4=0

x-8=0

Set the first factor equal to 0.

3x+4=0

Subtract 4 from both sides of the equation.

3x=-4

Divide each term by 3 and simplify.

Divide each term in 3x=-4 by 3.

3×3=-43

Cancel the common factor of 3.

Cancel the common factor.

3×3=-43

Divide x by 1.

x=-43

x=-43

Move the negative in front of the fraction.

x=-43

x=-43

x=-43

Set the next factor equal to 0.

x-8=0

Add 8 to both sides of the equation.

x=8

x=8

The final solution is all the values that make (3x+4)(x-8)=0 true.

x=-43,8

Solve using the Square Root Property 3x^2-20x-32=0