4y^2+66y+32=0

Solution for 4y^2+66y+32=0 equation:

Simplifying
4y2 + 66y + 32 = 0

Reorder the terms:
32 + 66y + 4y2 = 0

Solving
32 + 66y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 33y + 2y2) = 0

Factor a trinomial.
2((16 + y)(1 + 2y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + y)' equal to zero and attempt to solve:

Simplifying
16 + y = 0

Solving
16 + y = 0

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

Add '-16' to each side of the equation.
16 + -16 + y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + y = 0 + -16
y = 0 + -16

Combine like terms: 0 + -16 = -16
y = -16

Simplifying
y = -16
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 = {-16, -0.5}