4y^2=-6y-2

Solution for 4y^2=-6y-2 equation:

Simplifying
4y2 = -6y + -2

Reorder the terms:
4y2 = -2 + -6y

Solving
4y2 = -2 + -6y

Solving for variable 'y'.

Reorder the terms:
2 + 6y + 4y2 = -2 + -6y + 2 + 6y

Reorder the terms:
2 + 6y + 4y2 = -2 + 2 + -6y + 6y

Combine like terms: -2 + 2 = 0
2 + 6y + 4y2 = 0 + -6y + 6y
2 + 6y + 4y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
2 + 6y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3y + 2y2) = 0

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

Ignore the factor 2.
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 '(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 = {-1, -0.5}