3×2-17x+10=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⋅10=30 and whose sum is b=-17.

Factor -17 out of -17x.

3×2-17x+10=0

Rewrite -17 as -2 plus -15

3×2+(-2-15)x+10=0

Apply the distributive property.

3×2-2x-15x+10=0

3×2-2x-15x+10=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2-2x)-15x+10=0

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

x(3x-2)-5(3x-2)=0

x(3x-2)-5(3x-2)=0

Factor the polynomial by factoring out the greatest common factor, 3x-2.

(3x-2)(x-5)=0

(3x-2)(x-5)=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-2=0

x-5=0

Set the first factor equal to 0.

3x-2=0

Add 2 to both sides of the equation.

3x=2

Divide each term by 3 and simplify.

Divide each term in 3x=2 by 3.

3×3=23

Cancel the common factor of 3.

Cancel the common factor.

3×3=23

Divide x by 1.

x=23

x=23

x=23

x=23

Set the next factor equal to 0.

x-5=0

Add 5 to both sides of the equation.

x=5

x=5

The final solution is all the values that make (3x-2)(x-5)=0 true.

x=23,5

Solve Using the Square Root Property 3x^2-17x+10=0