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

-24X2-9X=0
Factor -3X out of -24X2-9X.
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 by -3 and simplify.
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+3X.
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 and solve.
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