24x^2+19xy-5y^2=

Solution for 24x^2+19xy-5y^2= equation:

Simplifying
24x2 + 19xy + -5y2 = 0

Reorder the terms:
19xy + 24x2 + -5y2 = 0

Solving
19xy + 24x2 + -5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(24x + -5y)(x + y) = 0

Subproblem 1
Set the factor '(24x + -5y)' equal to zero and attempt to solve:

Simplifying
24x + -5y = 0

Solving
24x + -5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '5y' to each side of the equation.
24x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
24x + 0 = 0 + 5y
24x = 0 + 5y
Remove the zero:
24x = 5y

Divide each side by '24'.
x = 0.2083333333y

Simplifying
x = 0.2083333333y
Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {0.2083333333y, -1y}