5y^2=13y+6

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Solution for 5y^2=13y+6 equation:


Simplifying
5y2 = 13y + 6

Reorder the terms:
5y2 = 6 + 13y

Solving
5y2 = 6 + 13y

Solving for variable 'y'.

Reorder the terms:
-6 + -13y + 5y2 = 6 + 13y + -6 + -13y

Reorder the terms:
-6 + -13y + 5y2 = 6 + -6 + 13y + -13y

Combine like terms: 6 + -6 = 0
-6 + -13y + 5y2 = 0 + 13y + -13y
-6 + -13y + 5y2 = 13y + -13y

Combine like terms: 13y + -13y = 0
-6 + -13y + 5y2 = 0

Factor a trinomial.
(-2 + -5y)(3 + -1y) = 0

Subproblem 1

Set the factor '(-2 + -5y)' equal to zero and attempt to solve: Simplifying -2 + -5y = 0 Solving -2 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5y = 0 + 2 -5y = 0 + 2 Combine like terms: 0 + 2 = 2 -5y = 2 Divide each side by '-5'. y = -0.4 Simplifying y = -0.4

Subproblem 2

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

Solution

y = {-0.4, 3}

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