30(y^2+1)=61y

Solution for 30(y^2+1)=61y equation:

Simplifying
30(y2 + 1) = 61y

Reorder the terms:
30(1 + y2) = 61y
(1 * 30 + y2 * 30) = 61y
(30 + 30y2) = 61y

Solving
30 + 30y2 = 61y

Solving for variable 'y'.

Reorder the terms:
30 + -61y + 30y2 = 61y + -61y

Combine like terms: 61y + -61y = 0
30 + -61y + 30y2 = 0

Factor a trinomial.
(5 + -6y)(6 + -5y) = 0

Subproblem 1
Set the factor '(5 + -6y)' equal to zero and attempt to solve:

Simplifying
5 + -6y = 0

Solving
5 + -6y = 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 + -6y = 0 + -5

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

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

Divide each side by '-6'.
y = 0.8333333333

Simplifying
y = 0.8333333333
Subproblem 2
Set the factor '(6 + -5y)' equal to zero and attempt to solve:

Simplifying
6 + -5y = 0

Solving
6 + -5y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -5y = 0 + -6

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

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

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {0.8333333333, 1.2}