3w^2+5w=-2

Solution for 3w^2+5w=-2 equation:

Simplifying
3w2 + 5w = -2

Reorder the terms:
5w + 3w2 = -2

Solving
5w + 3w2 = -2

Solving for variable 'w'.

Reorder the terms:
2 + 5w + 3w2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 5w + 3w2 = 0

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

Subproblem 1
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

Add '-1' to each side of the equation.
1 + -1 + w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + w = 0 + -1
w = 0 + -1

Combine like terms: 0 + -1 = -1
w = -1

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

Simplifying
2 + 3w = 0

Solving
2 + 3w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3w = 0 + -2
3w = 0 + -2

Combine like terms: 0 + -2 = -2
3w = -2

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {-1, -0.6666666667}