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
