15y^2-5z^2-22yz=0

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Solution for 15y^2-5z^2-22yz=0 equation:


Simplifying
15y2 + -5z2 + -22yz = 0

Reorder the terms:
-22yz + 15y2 + -5z2 = 0

Solving
-22yz + 15y2 + -5z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -5z)(5y + z) = 0

Subproblem 1

Set the factor '(3y + -5z)' equal to zero and attempt to solve: Simplifying 3y + -5z = 0 Solving 3y + -5z = 0 Move all terms containing y to the left, all other terms to the right. Add '5z' to each side of the equation. 3y + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 3y + 0 = 0 + 5z 3y = 0 + 5z Remove the zero: 3y = 5z Divide each side by '3'. y = 1.666666667z Simplifying y = 1.666666667z

Subproblem 2

Set the factor '(5y + z)' equal to zero and attempt to solve: Simplifying 5y + z = 0 Solving 5y + z = 0 Move all terms containing y to the left, all other terms to the right. Add '-1z' to each side of the equation. 5y + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 5y + 0 = 0 + -1z 5y = 0 + -1z Remove the zero: 5y = -1z Divide each side by '5'. y = -0.2z Simplifying y = -0.2z

Solution

y = {1.666666667z, -0.2z}

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