2(y^2+1)=5y

Solution for 2(y^2+1)=5y equation:

Simplifying
2(y2 + 1) = 5y

Reorder the terms:
2(1 + y2) = 5y
(1 * 2 + y2 * 2) = 5y
(2 + 2y2) = 5y

Solving
2 + 2y2 = 5y

Solving for variable 'y'.

Reorder the terms:
2 + -5y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
2 + -5y + 2y2 = 0

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

Subproblem 1
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0.5, 2}