4×2-15x+9=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=4⋅9=36 and whose sum is b=-15.

Factor -15 out of -15x.

4×2-15x+9=0

Rewrite -15 as -3 plus -12

4×2+(-3-12)x+9=0

Apply the distributive property.

4×2-3x-12x+9=0

4×2-3x-12x+9=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4×2-3x)-12x+9=0

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

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

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

Factor the polynomial by factoring out the greatest common factor, 4x-3.

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

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

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

4x-3=0

x-3=0

Set the first factor equal to 0.

4x-3=0

Add 3 to both sides of the equation.

4x=3

Divide each term by 4 and simplify.

Divide each term in 4x=3 by 4.

4×4=34

Cancel the common factor of 4.

Cancel the common factor.

4×4=34

Divide x by 1.

x=34

x=34

x=34

x=34

Set the next factor equal to 0.

x-3=0

Add 3 to both sides of the equation.

x=3

x=3

The final solution is all the values that make (4x-3)(x-3)=0 true.

x=34,3

Solve using the Square Root Property 4x^2-15x+9=0