5y^2=-7y-2

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

Simplifying
5y2 = -7y + -2

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

Solving
5y2 = -2 + -7y

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
2 + 5y = 0

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

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

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

Divide each side by '5'.
y = -0.4

Simplifying
y = -0.4
Solution
y = {-1, -0.4}