3×2=32-20x

Add 20x to both sides of the equation.

3×2+20x=32

Move 32 to the left side of the equation by subtracting it from both sides.

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+20(x)-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

Add 4 to 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

x=43

x=43

Set the next factor equal to 0.

x+8=0

Subtract 8 from 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=32-20x