-24X2-9X=0

Factor -3X out of -24X2.

-3X(8X)-9X=0

Factor -3X out of -9X.

-3X(8X)-3X⋅3=0

Factor -3X out of -3X(8X)-3X(3).

-3X(8X+3)=0

-3X(8X+3)=0

Divide each term in -3X(8X+3)=0 by -3.

-3X(8X+3)-3=0-3

Simplify -3X(8X+3)-3.

Simplify terms.

Cancel the common factor of -3.

Cancel the common factor.

-3X(8X+3)-3=0-3

Divide X(8X+3) by 1.

X(8X+3)=0-3

X(8X+3)=0-3

Apply the distributive property.

X(8X)+X⋅3=0-3

Reorder.

Rewrite using the commutative property of multiplication.

8X⋅X+X⋅3=0-3

Move 3 to the left of X.

8X⋅X+3⋅X=0-3

8X⋅X+3⋅X=0-3

8X⋅X+3⋅X=0-3

Multiply X by X by adding the exponents.

Move X.

8(X⋅X)+3⋅X=0-3

Multiply X by X.

8X2+3⋅X=0-3

8X2+3X=0-3

8X2+3X=0-3

Divide 0 by -3.

8X2+3X=0

8X2+3X=0

Factor X out of 8X2.

X(8X)+3X=0

Factor X out of 3X.

X(8X)+X⋅3=0

Factor X out of X(8X)+X⋅3.

X(8X+3)=0

X(8X+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.

X=0

8X+3=0

Set the first factor equal to 0.

X=0

Set the next factor equal to 0.

8X+3=0

Subtract 3 from both sides of the equation.

8X=-3

Divide each term by 8 and simplify.

Divide each term in 8X=-3 by 8.

8X8=-38

Cancel the common factor of 8.

Cancel the common factor.

8X8=-38

Divide X by 1.

X=-38

X=-38

Move the negative in front of the fraction.

X=-38

X=-38

X=-38

The final solution is all the values that make X(8X+3)=0 true.

X=0,-38

Solve using the Square Root Property -24X^2-9X=0