24y^2-10yz-25z^2=0

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Solution for 24y^2-10yz-25z^2=0 equation: 


Simplifying
24y2 + -10yz + -25z2 = 0

Reorder the terms:
-10yz + 24y2 + -25z2 = 0

Solving
-10yz + 24y2 + -25z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4y + -5z)(6y + 5z) = 0


Subproblem 1
Set the factor '(4y + -5z)' equal to zero and attempt to solve:

Simplifying
4y + -5z = 0

Solving
4y + -5z = 0

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

Add '5z' to each side of the equation.
4y + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
4y + 0 = 0 + 5z
4y = 0 + 5z
Remove the zero:
4y = 5z

Divide each side by '4'.
y = 1.25z

Simplifying
y = 1.25z

Subproblem 2
Set the factor '(6y + 5z)' equal to zero and attempt to solve:

Simplifying
6y + 5z = 0

Solving
6y + 5z = 0

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

Add '-5z' to each side of the equation.
6y + 5z + -5z = 0 + -5z

Combine like terms: 5z + -5z = 0
6y + 0 = 0 + -5z
6y = 0 + -5z
Remove the zero:
6y = -5z

Divide each side by '6'.
y = -0.8333333333z

Simplifying
y = -0.8333333333z
Solution
y = {1.25z, -0.8333333333z}

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