=3y^2+10y+3

Solution for =3y^2+10y+3 equation:

Simplifying
0 = 3y2 + 10y + 3

Reorder the terms:
0 = 3 + 10y + 3y2

Solving
0 = 3 + 10y + 3y2

Solving for variable 'y'.

Combine like terms: 0 + -3 = -3
-3 + -10y + -3y2 = 3 + 10y + 3y2 + -3 + -10y + -3y2

Reorder the terms:
-3 + -10y + -3y2 = 3 + -3 + 10y + -10y + 3y2 + -3y2

Combine like terms: 3 + -3 = 0
-3 + -10y + -3y2 = 0 + 10y + -10y + 3y2 + -3y2
-3 + -10y + -3y2 = 10y + -10y + 3y2 + -3y2

Combine like terms: 10y + -10y = 0
-3 + -10y + -3y2 = 0 + 3y2 + -3y2
-3 + -10y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-3 + -10y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 10y + 3y2) = 0

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

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
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 = {-3, -0.3333333333}