5z^2-37zy+42y^2=0

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Solution for 5z^2-37zy+42y^2=0 equation: 


Simplifying
5z2 + -37zy + 42y2 = 0

Reorder the terms:
-37yz + 42y2 + 5z2 = 0

Solving
-37yz + 42y2 + 5z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(7y + -5z)(6y + -1z) = 0


Subproblem 1
Set the factor '(7y + -5z)' equal to zero and attempt to solve:

Simplifying
7y + -5z = 0

Solving
7y + -5z = 0

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

Add '5z' to each side of the equation.
7y + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
7y + 0 = 0 + 5z
7y = 0 + 5z
Remove the zero:
7y = 5z

Divide each side by '7'.
y = 0.7142857143z

Simplifying
y = 0.7142857143z

Subproblem 2
Set the factor '(6y + -1z)' equal to zero and attempt to solve:

Simplifying
6y + -1z = 0

Solving
6y + -1z = 0

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

Add 'z' to each side of the equation.
6y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
6y + 0 = 0 + z
6y = 0 + z
Remove the zero:
6y = z

Divide each side by '6'.
y = 0.1666666667z

Simplifying
y = 0.1666666667z
Solution
y = {0.7142857143z, 0.1666666667z}

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