-7y=2y^2+5

Solution for -7y=2y^2+5 equation:

Simplifying
-7y = 2y2 + 5

Reorder the terms:
-7y = 5 + 2y2

Solving
-7y = 5 + 2y2

Solving for variable 'y'.

Reorder the terms:
-5 + -7y + -2y2 = 5 + 2y2 + -5 + -2y2

Reorder the terms:
-5 + -7y + -2y2 = 5 + -5 + 2y2 + -2y2

Combine like terms: 5 + -5 = 0
-5 + -7y + -2y2 = 0 + 2y2 + -2y2
-5 + -7y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-5 + -7y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 7y + 2y2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 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 + 2y = 0 + -5

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

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

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {-2.5, -1}