5(y^2-76)=-81y

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Solution for 5(y^2-76)=-81y equation:


Simplifying
5(y2 + -76) = -81y

Reorder the terms:
5(-76 + y2) = -81y
(-76 * 5 + y2 * 5) = -81y
(-380 + 5y2) = -81y

Solving
-380 + 5y2 = -81y

Solving for variable 'y'.

Reorder the terms:
-380 + 81y + 5y2 = -81y + 81y

Combine like terms: -81y + 81y = 0
-380 + 81y + 5y2 = 0

Factor a trinomial.
(-20 + -1y)(19 + -5y) = 0

Subproblem 1

Set the factor '(-20 + -1y)' equal to zero and attempt to solve: Simplifying -20 + -1y = 0 Solving -20 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1y = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1y = 0 + 20 -1y = 0 + 20 Combine like terms: 0 + 20 = 20 -1y = 20 Divide each side by '-1'. y = -20 Simplifying y = -20

Subproblem 2

Set the factor '(19 + -5y)' equal to zero and attempt to solve: Simplifying 19 + -5y = 0 Solving 19 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -5y = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -5y = 0 + -19 -5y = 0 + -19 Combine like terms: 0 + -19 = -19 -5y = -19 Divide each side by '-5'. y = 3.8 Simplifying y = 3.8

Solution

y = {-20, 3.8}

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