2y^2+7=5-5y

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

Simplifying
2y2 + 7 = 5 + -5y

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

Solving
7 + 2y2 = 5 + -5y

Solving for variable 'y'.

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

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

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

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

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

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

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

Simplifying
2 + y = 0

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

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

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

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