2×2+3x-20=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=2⋅-20=-40 and whose sum is b=3.

Factor 3 out of 3x.

2×2+3(x)-20=0

Rewrite 3 as -5 plus 8

2×2+(-5+8)x-20=0

Apply the distributive property.

2×2-5x+8x-20=0

2×2-5x+8x-20=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2-5x)+8x-20=0

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

x(2x-5)+4(2x-5)=0

x(2x-5)+4(2x-5)=0

Factor the polynomial by factoring out the greatest common factor, 2x-5.

(2x-5)(x+4)=0

(2x-5)(x+4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x-5=0

x+4=0

Set the first factor equal to 0.

2x-5=0

Add 5 to both sides of the equation.

2x=5

Divide each term by 2 and simplify.

Divide each term in 2x=5 by 2.

2×2=52

Cancel the common factor of 2.

Cancel the common factor.

2×2=52

Divide x by 1.

x=52

x=52

x=52

x=52

Set the next factor equal to 0.

x+4=0

Subtract 4 from both sides of the equation.

x=-4

x=-4

The final solution is all the values that make (2x-5)(x+4)=0 true.

x=52,-4

Solve Using the Square Root Property 2x^2+3x-20=0