42y^2+32y+6=

Solution for 42y^2+32y+6= equation:

Simplifying
42y2 + 32y + 6 = 0

Reorder the terms:
6 + 32y + 42y2 = 0

Solving
6 + 32y + 42y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 16y + 21y2) = 0

Factor a trinomial.
2((3 + 7y)(1 + 3y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 7y)' equal to zero and attempt to solve:

Simplifying
3 + 7y = 0

Solving
3 + 7y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7y = 0 + -3
7y = 0 + -3

Combine like terms: 0 + -3 = -3
7y = -3

Divide each side by '7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 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 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {-0.4285714286, -0.3333333333}