5×2+17x-12=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=5⋅-12=-60 and whose sum is b=17.

Factor 17 out of 17x.

5×2+17(x)-12=0

Rewrite 17 as -3 plus 20

5×2+(-3+20)x-12=0

Apply the distributive property.

5×2-3x+20x-12=0

5×2-3x+20x-12=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5×2-3x)+20x-12=0

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

x(5x-3)+4(5x-3)=0

x(5x-3)+4(5x-3)=0

Factor the polynomial by factoring out the greatest common factor, 5x-3.

(5x-3)(x+4)=0

(5x-3)(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.

5x-3=0

x+4=0

Set the first factor equal to 0.

5x-3=0

Add 3 to both sides of the equation.

5x=3

Divide each term by 5 and simplify.

Divide each term in 5x=3 by 5.

5×5=35

Cancel the common factor of 5.

Cancel the common factor.

5×5=35

Divide x by 1.

x=35

x=35

x=35

x=35

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 (5x-3)(x+4)=0 true.

x=35,-4

Solve Using the Square Root Property 5x^2+17x-12=0