6y^2=-42-87y

Solution for 6y^2=-42-87y equation:

Simplifying
6y2 = -42 + -87y

Solving
6y2 = -42 + -87y

Solving for variable 'y'.

Reorder the terms:
42 + 87y + 6y2 = -42 + -87y + 42 + 87y

Reorder the terms:
42 + 87y + 6y2 = -42 + 42 + -87y + 87y

Combine like terms: -42 + 42 = 0
42 + 87y + 6y2 = 0 + -87y + 87y
42 + 87y + 6y2 = -87y + 87y

Combine like terms: -87y + 87y = 0
42 + 87y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 29y + 2y2) = 0

Factor a trinomial.
3((14 + y)(1 + 2y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(14 + y)' equal to zero and attempt to solve:

Simplifying
14 + y = 0

Solving
14 + y = 0

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

Add '-14' to each side of the equation.
14 + -14 + y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + y = 0 + -14
y = 0 + -14

Combine like terms: 0 + -14 = -14
y = -14

Simplifying
y = -14
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 = {-14, -0.5}