3y^2=-16y-5

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Solution for 3y^2=-16y-5 equation:


Simplifying
3y2 = -16y + -5

Reorder the terms:
3y2 = -5 + -16y

Solving
3y2 = -5 + -16y

Solving for variable 'y'.

Reorder the terms:
5 + 16y + 3y2 = -5 + -16y + 5 + 16y

Reorder the terms:
5 + 16y + 3y2 = -5 + 5 + -16y + 16y

Combine like terms: -5 + 5 = 0
5 + 16y + 3y2 = 0 + -16y + 16y
5 + 16y + 3y2 = -16y + 16y

Combine like terms: -16y + 16y = 0
5 + 16y + 3y2 = 0

Factor a trinomial.
(5 + y)(1 + 3y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333

Solution

y = {-5, -0.3333333333}

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