3w^2=-5w+2

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

Simplifying
3w2 = -5w + 2

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

Solving
3w2 = 2 + -5w

Solving for variable 'w'.

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

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

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

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

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

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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 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 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

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

Simplifying
1 + -3w = 0

Solving
1 + -3w = 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 + -3w = 0 + -1

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

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

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

Simplifying
w = 0.3333333333
Solution
w = {-2, 0.3333333333}