24×2-5x-36=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=24⋅-36=-864 and whose sum is b=-5.

Factor -5 out of -5x.

24×2-5x-36=0

Rewrite -5 as 27 plus -32

24×2+(27-32)x-36=0

Apply the distributive property.

24×2+27x-32x-36=0

24×2+27x-32x-36=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(24×2+27x)-32x-36=0

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

3x(8x+9)-4(8x+9)=0

3x(8x+9)-4(8x+9)=0

Factor the polynomial by factoring out the greatest common factor, 8x+9.

(8x+9)(3x-4)=0

(8x+9)(3x-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.

8x+9=0

3x-4=0

Set the first factor equal to 0.

8x+9=0

Subtract 9 from both sides of the equation.

8x=-9

Divide each term by 8 and simplify.

Divide each term in 8x=-9 by 8.

8×8=-98

Cancel the common factor of 8.

Cancel the common factor.

8×8=-98

Divide x by 1.

x=-98

x=-98

Move the negative in front of the fraction.

x=-98

x=-98

x=-98

Set the next factor equal to 0.

3x-4=0

Add 4 to both sides of the equation.

3x=4

Divide each term by 3 and simplify.

Divide each term in 3x=4 by 3.

3×3=43

Cancel the common factor of 3.

Cancel the common factor.

3×3=43

Divide x by 1.

x=43

x=43

x=43

x=43

The final solution is all the values that make (8x+9)(3x-4)=0 true.

x=-98,43

Solve Using the Square Root Property 24x^2-5x-36=0