3y^2+5yz-2z^2=

Solution for 3y^2+5yz-2z^2= equation:

Simplifying
3y2 + 5yz + -2z2 = 0

Reorder the terms:
5yz + 3y2 + -2z2 = 0

Solving
5yz + 3y2 + -2z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -1z)(y + 2z) = 0

Subproblem 1
Set the factor '(3y + -1z)' equal to zero and attempt to solve:

Simplifying
3y + -1z = 0

Solving
3y + -1z = 0

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

Add 'z' to each side of the equation.
3y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
3y + 0 = 0 + z
3y = 0 + z
Remove the zero:
3y = z

Divide each side by '3'.
y = 0.3333333333z

Simplifying
y = 0.3333333333z
Subproblem 2
Set the factor '(y + 2z)' equal to zero and attempt to solve:

Simplifying
y + 2z = 0

Solving
y + 2z = 0

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

Add '-2z' to each side of the equation.
y + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
y + 0 = 0 + -2z
y = 0 + -2z
Remove the zero:
y = -2z

Simplifying
y = -2z
Solution
y = {0.3333333333z, -2z}