=8y^2-18yz-5z^2

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Solution for =8y^2-18yz-5z^2 equation:


Simplifying
0 = 8y2 + -18yz + -5z2

Reorder the terms:
0 = -18yz + 8y2 + -5z2

Solving
0 = -18yz + 8y2 + -5z2

Solving for variable 'y'.
Remove the zero:
18yz + -8y2 + 5z2 = -18yz + 8y2 + -5z2 + 18yz + -8y2 + 5z2

Reorder the terms:
18yz + -8y2 + 5z2 = -18yz + 18yz + 8y2 + -8y2 + -5z2 + 5z2

Combine like terms: -18yz + 18yz = 0
18yz + -8y2 + 5z2 = 0 + 8y2 + -8y2 + -5z2 + 5z2
18yz + -8y2 + 5z2 = 8y2 + -8y2 + -5z2 + 5z2

Combine like terms: 8y2 + -8y2 = 0
18yz + -8y2 + 5z2 = 0 + -5z2 + 5z2
18yz + -8y2 + 5z2 = -5z2 + 5z2

Combine like terms: -5z2 + 5z2 = 0
18yz + -8y2 + 5z2 = 0

Factor a trinomial.
(-4y + -1z)(2y + -5z) = 0

Subproblem 1

Set the factor '(-4y + -1z)' equal to zero and attempt to solve: Simplifying -4y + -1z = 0 Solving -4y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. -4y + -1z + z = 0 + z Combine like terms: -1z + z = 0 -4y + 0 = 0 + z -4y = 0 + z Remove the zero: -4y = z Divide each side by '-4'. y = -0.25z Simplifying y = -0.25z

Subproblem 2

Set the factor '(2y + -5z)' equal to zero and attempt to solve: Simplifying 2y + -5z = 0 Solving 2y + -5z = 0 Move all terms containing y to the left, all other terms to the right. Add '5z' to each side of the equation. 2y + -5z + 5z = 0 + 5z Combine like terms: -5z + 5z = 0 2y + 0 = 0 + 5z 2y = 0 + 5z Remove the zero: 2y = 5z Divide each side by '2'. y = 2.5z Simplifying y = 2.5z

Solution

y = {-0.25z, 2.5z}

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