8y=13y^2-5

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Solution for 8y=13y^2-5 equation:


Simplifying
8y = 13y2 + -5

Reorder the terms:
8y = -5 + 13y2

Solving
8y = -5 + 13y2

Solving for variable 'y'.

Reorder the terms:
5 + 8y + -13y2 = -5 + 13y2 + 5 + -13y2

Reorder the terms:
5 + 8y + -13y2 = -5 + 5 + 13y2 + -13y2

Combine like terms: -5 + 5 = 0
5 + 8y + -13y2 = 0 + 13y2 + -13y2
5 + 8y + -13y2 = 13y2 + -13y2

Combine like terms: 13y2 + -13y2 = 0
5 + 8y + -13y2 = 0

Factor a trinomial.
(1 + -1y)(5 + 13y) = 0

Subproblem 1

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Subproblem 2

Set the factor '(5 + 13y)' equal to zero and attempt to solve: Simplifying 5 + 13y = 0 Solving 5 + 13y = 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 + 13y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 13y = 0 + -5 13y = 0 + -5 Combine like terms: 0 + -5 = -5 13y = -5 Divide each side by '13'. y = -0.3846153846 Simplifying y = -0.3846153846

Solution

y = {1, -0.3846153846}

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