3=3×2-5x+5

Rewrite the equation as 3×2-5x+5=3.

3×2-5x+5=3

Move 3 to the left side of the equation by subtracting it from both sides.

3×2-5x+5-3=0

Subtract 3 from 5.

3×2-5x+2=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⋅2=6 and whose sum is b=-5.

Factor -5 out of -5x.

3×2-5x+2=0

Rewrite -5 as -2 plus -3

3×2+(-2-3)x+2=0

Apply the distributive property.

3×2-2x-3x+2=0

3×2-2x-3x+2=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2-2x)-3x+2=0

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

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

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

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

(3x-2)(x-1)=0

(3x-2)(x-1)=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-1=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-1=0

Add 1 to both sides of the equation.

x=1

x=1

The final solution is all the values that make (3x-2)(x-1)=0 true.

x=23,1

Solve using the Square Root Property 3=3x^2-5x+5