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

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}